Silicon nitride waveguide optical filter components for access network applications

by

Saurabh BEDI

THESIS PRESENTED TO ÉCOLE DE TECHNOLOGIE SUPÉRIEURE IN PARTIAL FULFILLMENT FOR A MASTER’S DEGREE

WITH THESIS IN ELECTRICAL ENGINEERING M.A.Sc

MONTREAL, OCTOBER 19, 2018

ÉCOLE DE TECHNOLOGIE SUPÉRIEURE UNIVERSITÉ DU QUÉBEC

(Saurabh Bedi, 2018)

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BOARD OF EXAMINERS (THESIS M.A.SC.)

THIS THESIS HAS BEEN EVALUATED

BY THE FOLLOWING BOARD OF EXAMINERS Mr. Frédéric Nabki, Thesis Supervisor Department of Electrical Engineering, École de technologie supérieure Mr. Michaël Ménard, Thesis Co-supervisor Computer Science Department, Université du Québec à Montréal Mr. Ricardo Izquierdo, Chair, Board of Examiners Department of Electrical Engineering, École de technologie supérieure Mr. Bora Ung, Evaluator Department of Electrical Engineering, École de technologie supérieure

THIS THESIS WAS PRENSENTED AND DEFENDED

IN THE PRESENCE OF A BOARD OF EXAMINERS AND PUBLIC

SEPTEMBER 28TH, 2018

AT ÉCOLE DE TECHNOLOGIE SUPÉRIEURE

ACKNOWLEDGMENT

Firstly, I would like to thank my family for their unceasing support, encouragement and faith

throughout my period of study. Their unwavering support has helped me throughout my studies

since childhood until now. Secondly, I would like to thank few individuals without whom this

project would have not been successful. Their constant help and supervision have helped me

reshaping my thesis and evolved me as a researcher. I sincerely thank my supervisor Prof.

Frederic Nabki (ETS) and my co-supervisor Prof. Michael Menard (UQAM) for their

unwavering support, faith and guidance throughout my research project. Their assistance has

been profitable from time to time and have been enlightening during the difficult times. Their

faith in me have pushed me through my difficult times. Thirdly, I would like to thank Mr.

Francois Menard and Mr. Philippe Babin from our industrial partner AEPONYX for believing

in me and trusting me with this challenging research work. My research team members from

CoFaMic research center, UQAM who have helped me in the fabrication and characterization

of my design chips. I would personally like to give a quote of thanks to Dr. Menouer Saidani

for helping me out in fabricating my device structures, Dr. Hadi Rabbani Haghighi for his

technical guidance and sharing his expertise in the field of optics during the initial period my

master thesis, Dr. Mohannad Alsayed for being the fabrication expert of our group and advising

about the fab techniques and constraints. My wife Sakshi Jain whose constant support and love

has pushed me this far and has helped me during the challenging time of my research. My

colleagues Mr. Suraj Sharma (PhD student) working on MEMS platform for his moral support

throughout my research period and Mr. Belaid Tabti (Master student) at UQAM for his support

and knowledge exchange during the technical projects and while my initial challenging phase

with measurements of the devices. Their consistent support has allowed me to finish my time-

bound projects and to achieve my targets within the research timeline. Also, I would like to

acknowledge some other personnel’s who have been a healthy part of my journey, in one way

or the other, during my master thesis project such as Dr. Michiel Soer (CoFaMic), Mrs. Anubha

Gupta Soer (PhD student), Mr. Shivaram Arun (PhD student), Mrs. Devika Padamkumar Nair

(PhD student) for their light hearted conversations over coffee and maintaining an incredible

research environment.

VI

I gratefully acknowledge the support of the National Sciences and Engineering Research

Council (NSERC) of Canada. Also, I would take this opportunity to thank our other research

partners such as Regroupement Stratégique en Microsystèmes du Québec (RESMIQ) and

Centre d’ Optique, Photonique et Laser (COPL). In the end, I would like to acknowledge CMC

Microsystems for the provision of services that facilitated this research and Lumerical

Solutions, Inc. for providing the design tools

SILICON NITRDE WAVEGUIDE OPTICAL FILTER COMPONENTS FOR ACCESS NETWORK APPLICATIONS

Saurabh BEDI

ABSTRACT

Silicon nitride (SiN) waveguide based micro ring/racetrack resonators to be used as filters in the Chirp Managed Lasers (CMLs) are modelled and demonstrated over the standard silicon (Si) wafer. The development of these racetrack-resonators, with a narrow free spectral range (FSR) of 100GHz is in correspondence to the international telecommunication union (ITU) recommended channel grid spacing required for the latest next generation passive optical networks (NGPON2) systems. The study of such optical filters, which tend to increase the transmission range of the directly modulated laser (DML) signal, is motivated from the research and development directed towards bringing the CMLs to a reality. Also, a single SiN ring resonator and a silicon waveguide based cascaded 3-ring design, both integrated within the Y-splitter configuration are presented to be used as a reflector in external cavity laser. These ring reflectors are designed to have a broad FSR, which is achieved using the Vernier effect by serially coupling three racetrack resonators. In this thesis, we analyze and optimize the optical response of the above mentioned devices based on SiN waveguides deposited over silicon wafers. The design parameters are optimized based on analytical modelling and simulations are carried out with finite difference time domain (FDTD) solver. The devices are fabricated in different labs and clean room facilities within Montreal in collaboration with our industrial partner AEPONYX. The performance of these fabricated devices is characterized using an optical test setup in university lab facilities. The simulation and the measurement results are in close proximity for a large 4-port add-drop racetrack resonator, giving a FSR close to 100GHz specified for the NGPON2 systems and an extinction ratio (ER) of >15 dB to be useful for modulating the inherent chirp of the directly modulated lasers (DML) and thereby increasing the transmission range of the data signals. For the Si waveguide based cascaded 3rd order ring reflector, a wide FSR of 90.2 nm is achieved numerically and a FSR of around ~6.02 nm is demonstrated for the SiN single ring reflector experimentally which is in close proximity to the theoretical value of 6.2 nm. Keywords: ring resonator, silicon nitride waveguide, chirp managed laser, Vernier effect, NGPON-2, ring reflector.

FILTRES OPTIQUES EN NITRURE DE SILICIUM POUR APPLICATIONS DANS

LES RESEAUX D'ACCES

Saurabh BEDI

RÉSUMÉ

Des micro-résonateurs en anneau à base de guide d’onde en nitrure de silicium (SiN) sont modélisés et fabriqués sur une tranche de silicium (Si) afin d’être utilisés comme filtre dans des lasers conçus pour la modulation exaltée par le chirp (CMLs). Le développement de ces résonateurs, avec une plage spectrale libre (FSR) de 100 GHz correspondant à l'espacement des canaux recommandé par l'union internationale des télécommunications (ITU), est envisagé pour la prochaine génération des systèmes de réseaux optiques passifs (NGPON2). L'étude de tels filtres optiques, qui augmente la portée de transmission du signal laser modulé directement (DML), est motivée par la recherche et le développement orientés vers la réalisation des CMLs. De plus, un résonateur en anneau en SiN simple et une autre incluant trois anneaux en cascade à base de guide d'ondes de silicium, tous deux intégrés avec un séparateur en Y, sont présentés pour être utilisés comme réflecteur dans un laser à cavité externe. Ces réflecteurs annulaires sont conçus pour avoir un FSR large, qui est réalisé en utilisant l'effet de Vernier en couplant trois résonateurs de circuit en série. Dans cette thèse, nous analysons et optimisons la réponse optique des dispositifs mentionnés ci-dessus à base de guides d'ondes SiN déposés sur des plaquettes de silicium. Les paramètres de conception sont optimisés à partir d’une modélisation analytique et des simulations sont effectuées avec un algorithme des différences finies dans le domaine temporel (FDTD). Les composants sont fabriqués dans différents laboratoires et salles blanches à Montréal en collaboration avec notre partenaire industriel AEPONYX. La performance de ces dispositifs est caractérisée en utilisant un banc d'essai optique dans les laboratoires universitaires. Une bonne correspondance est observée entre les résultats de simulations et les mesures d'un grand résonateur de circuit à 4 ports, donnant un FSR proche de 100GHz tel que spécifié pour les systèmes NGPON2 et un taux d'extinction (ER) de plus de 15 dB. Cela rend ce composant utile pour moduler le chirp inhérent des lasers modulés directement (DML), augmentant ainsi le ratio d’extinction des signaux de données. Pour le réflecteur annulaire de troisième ordre en cascade à base de guide d'onde en Si, un large FSR de 90,2 nm est atteint numériquement et un FSR d'environ 6,02 nm est démontré expérimentalement pour le réflecteur à un seul anneau en SiN, ce qui est très proche de la valeur théorique de 6,2 nm. Mots-clés: résonateur en anneau, guide d'onde en nitrure de silicium, chirp géré laser, l'effet de Vernier, NGPON-2, anneau réflecteur.

TABLE OF CONTENTS

Page INTRODUCTION .....................................................................................................................1 CHAPTER 1 SILICON PHOTONICS IN OPTICAL COMMUNICATION .......................3 1.1 Thesis Objective ............................................................................................................ 4 1.2 Methodology .................................................................................................................. 5 1.3 Thesis Contributions ...................................................................................................... 6 1.4 Thesis Organization ....................................................................................................... 7 CHAPTER 2 PASSIVE OPTICAL FILTERS: A LITERATURE REVIEW .......................9 2.1 Microring Resonators for Transceiver Applications .................................................... 10 2.2 Microdisk Resonators for Transceiver Applications ................................................... 22 2.3 Silicon nitride waveguide based Microring and Microdisk Resonators ...................... 25 CHAPTER 3 RING-REFLECTOR FOR TUNABLE LASER APPLICATION ................29 3.1 Design Approach ......................................................................................................... 31 3.2 Simulations and Optimization...................................................................................... 33

3.2.1 Simulation of a channel waveguide .......................................................... 33 3.2.2 Simulation of a Directional Coupler ......................................................... 36 3.2.3 Simulation of a Silicon Nitride Ring Reflector ......................................... 37 3.2.4 Simulation of a Silicon Serially Coupled 3-Ring Reflector:

The Vernier Effect .................................................................................... 41 3.3 Fabrication, Measurements and Analysis .................................................................... 48

3.3.1 Mask Layout Description .......................................................................... 48 3.3.2 Fabrication Process Flow for Si3N4 structures. ......................................... 49 3.3.3 Optical Test Setup ..................................................................................... 50 3.3.4 Measurements and Analysis ..................................................................... 52

3.4 Summary ...................................................................................................................... 61 CHAPTER 4 RACETRACK RESONATOR FOR THE CHIRPED

MODULATED LASER...................................................................................63 4.1 Small 4-port add-drop racetrack resonator .................................................................. 66

4.1.1 Design, Simulation and Optimization ....................................................... 66 4.1.2 Fabrication, Measurements and Analysis ................................................. 74

4.2 Large 4-port add-drop racetrack resonator .................................................................. 78 4.2.1 Design, Simulation and Optimization ....................................................... 78 4.2.2 Fabrication, Measurements and Analysis ................................................. 84

4.3 Summary ...................................................................................................................... 87 CONCLUSIONS AND FUTURE WORK ..............................................................................89

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APPENDIX I Derivation for power equations of racetrack resonator ................................. 91 APPENDIX II Derivation of 3rd order ring filter .................................................................. 95 APPENDIX III Derivation of relation between effective refractive index n(r,ϕ) and

field function (ψ) ........................................................................................... 97 APPENDIX IV MATLAB script for computing optical response of ring-resonator ............. 99 APPENDIX V MATLAB script for computing of cut-off thickness ................................. 101 BIBLIOGRAPHY ................................................................................................................. 103

LIST OF TABLES

Page

Table 3.1 Parameters of different RRs (based on Si waveguide) integrated

with Y-splitters ........................................................................................... 41

Table 3.2 Attributes obtained for Si waveguide based three different ring reflectors ..................................................................................................... 43

Table 3.3 Optimized design parameters for Si waveguide based three different single ring reflectors ................................................................................... 45

Table 3.4 Performance parameters for the optimized single Si ring reflectors .......... 46

Table 3.5 Important attributes illustrating fabricated device performance ................ 54

Table 3.6 Cut-off thickness for the waveguide structure ........................................... 59

Table 4.1 Design parameters for two different racetrack-resonators ......................... 72

Table 4.2 Performance attributes for two different racetrack-resonators ................... 74

LIST OF FIGURES

Page

Figure 1.1 Performance of the top 500 supercomputers in the world ........................... 3

Figure 1.2 Research cycle .............................................................................................. 5

Figure 2.1 Field propagation along a directional coupler. Modes calculated using the waveguide mode solver and the modes are propagated using the eigenmode expansion method ..................................................... 12

Figure 2.2 Model of a (a) single ring resonator with one waveguide, which forms a ‘notch filter’ and (b) the basic add-drop ring resonator filter .................................................................................................................... 13

Figure 2.3 Model of a serially coupled three-ring add-drop filter showing the coupling coefficients and the loss coefficients for each ring ..................... 18

Figure 2.4 A general schematic of an external cavity semiconductor laser ................ 20

Figure 2.5 a) Schematic of the ring with integrated DBR. The DBR is realized by modulating the top half of the ring waveguide. b) SEM image of the fabricated device prior to top cladding deposition ............................... 21

Figure 3.1 A general schematic of a wavelength tunable laser electromechanically tuned using a MEMS actuator ................................... 29

Figure 3.2 Schematic of the proposed 3-ring reflector filter having racetrack-

resonator serially coupled and integrated with two Y-branch splitters showing propagation of the reflected and the transmitted light within the filter ................................................................................... 31

Figure 3.3 (a) Perspective view of Si3N4 channel waveguide with insets

showing the cross-section waveguide geometry and TE mode distribution; (b) Wavelength dependent effective index (c) Wavelength dependent group index ........................................................... 34

Figure 3.4 (a) Perspective view of Si channel waveguide with insets showing

the cross-section waveguide geometry and TE mode distribution; (b) Wavelength dependent effective index; (c) Wavelength dependent group index ............................................................................... 35

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Figure 3.5 The effect of waveguide width variation over neff and ng at 1550 nm for (a) Silicon nitride waveguide (thickness of 435 nm), (b) Silicon waveguide (thickness of 220 nm) ............................................................... 35

Figure 3.6 Symmetric and Antisymmetric modes dependence over the

coupling gap at 1550 nm for (a) Si3N4 waveguide (b) Si waveguide;with insets showing supermodes electric field distribution ................................................................................................. 36

Figure 3.7 Field coupling coefficient ‘k’ versus coupling gap at 1550 nm for

(a) Silicon nitride waveguide having dimensions 435 nm x 435 nm (L=20 μm), and (b) Silicon waveguide having dimensions 440 nm x 220 nm (L=20 μm) .................................................................................. 36

Figure 3.8 General schematic of a single ring reflector based on Si3N4 waveguide with dimensions 435 nm x 435 nm .......................................... 38

Figure 3.9 Waveguide bend loss versus radius for 435 nm wide Si3N4

waveguide (in dB scale) ............................................................................. 38 Figure 3.10 Effect of field coupling coefficient κ on the drop port peak intensity

of an add-drop ring resonator ..................................................................... 39

Figure 3.11 (a) Simulated spectral response of a silicon nitride single ring reflector, (b) zoom in of the resonance peak of the reflection/drop port response .............................................................................................. 40

Figure 3.12 FSRs for three different ring reflectors, each of them showing a

common central wavelength around ~1492 nm ......................................... 42

Figure 3.13 The reflection response of a serially coupled 3-ring reflector in a 2.5D-FDTD showing resonance peak splitting .......................................... 43

Figure 3.14 The effect of the coupling coefficient ‘κ’ on the drop port peak intensity of Si waveguide based single ring resonator of radius (a) 3.6 μm (b) 4.3 μm and (c) 10 μm ............................................................... 45

Figure 3.15 Reflection spectra obtained from 2.5D-FDTD for three different Si ring reflectors showing their corresponding FSRs ..................................... 46

Figure 3.16 Reflection spectra for a serially coupled Si 3-ring filter illustrating the Vernier effect and showing the dominant resonant peak without peak splitting .............................................................................................. 47

Figure 3.17 A generalised process flow for the fabrication of the Si3N4 waveguide structures .................................................................................. 50

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Figure 3.18 Optical Test Measurement Setup (1) (a) Single mode input fibre (b) Single mode output fibre (2) Device chip (3) Chip holding stage (4) Chip stage controller (5) Three axis stage controller for (a) input fibre (b) output fibre (6) Polarization rotator (7) Microscope .................... 51

Figure 3.19 The through port transmission response for (a) Device 6, (b) Device 8 & (c) Device 9 ......................................................................................... 53

Figure 3.20 Comparison of the through port transmission response for 3 devices .................................................................................................................... 55

Figure 3.21 (a) Theoretical vs Experimental through port response for devices 6, 8 and 9 (b) Zoomed in response of plot (a) ............................................ 56

Figure 3.22 SEM image of the (a) fabricated waveguides forming the coupling region and (b) the cross section of the waveguide ..................................... 57

Figure 3.23 Normalized curve showing theoretical vs experimental response for varying widths (a) Device 6 (435 nm) (b) Device 8 (445 nm) (c) Device 9 (455 nm) ...................................................................................... 59

Figure 3.24 The effect on the neff of the fundamental TE and TM mode for the (a) Fabricated waveguide width (386 μm top x 427 bottom) vs. the varying waveguide thickness and (b) Fabricated waveguide thickness of 453 μm vs. the varying waveguide width .............................. 60

Figure 4.1 (a) Electrical signal at the input, and a distorted (b) optical signal at the output, of a DML due to chirp .............................................................. 64

Figure 4.2 Change of instantaneous frequency ωinst with time showing blue and red shift ....................................................................................................... 65

Figure 4.3 (a) Perspective view of a Si3N4 channel waveguide with insets showing the cross-section waveguide geometry and fundamental TE & TM mode distribution; (b) Wavelength dependent effective index for TE mode (c) Wavelength dependent group index for TE mode (d) Wavelength dependent effective index for TM mode (e) Wavelength dependent group index for TM mode .................................... 68

Figure 4.4 The fabrication tolerance showing the change in the neff of fundamental TE and TM mode at 1550 nm due to (a) variation in the width (fixed thickness at 400 nm) (b) variation in the thickness (fixed width at 400 nm) .............................................................................. 68

Figure 4.5 Field coupling coefficient ‘κ’ vs gap, λ=1550 nm, coupler length L=5 μm, L=10 μm, L=15 μm and L=20 μm, 400 nm x 400 nm

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waveguide, calculated using the waveguide mode solver with a 10 nm mesh size .............................................................................................. 69

Figure 4.6 The neff of symmetric and antisymmetric modes versus the coupling gap, λ= 1550 nm, 400 nm x 400 nm Si3N4 waveguide. ............................. 70

Figure 4.7 Waveguide bend loss vs. radius for 400 nm wide SiN waveguide (in dB scale), bend angle of 900 ....................................................................... 71

Figure 4.8 The schematic design of two different racetrack resonators (a) Type A, (b) Type B ............................................................................................. 72

Figure 4.9 Simulated optical response for type A racetrack-resonator........................ 73

Figure 4.10 Simulated optical response for type B racetrack-resonator ........................ 73

Figure 4.11 The intensity profile of the light propagating inside the racetrack resonator obtained using 2.5D-FDTD simulations in Lumerical MODE ........................................................................................................ 74

Figure 4.12 Transmission spectra for a small ring filter, waveguide 400 nm x 400 nm ........................................................................................................ 76

Figure 4.13 SEM image of (a) the fabricated RR and (b) the coupling region of RR showing variation in the gap and the waveguide widths. .................... 77

Figure 4.14 Field coupling coefficient ‘κ’ vs gap, λ=1550 nm, coupler length L=10 μm, L=15 μm, L=20 μm, L=25, L=30 μm and L=35 μm, 435 nm x 435 nm waveguide, calculated using the waveguide mode solver with a 10 nm mesh size. .................................................................. 79

Figure 4.15 The general schematic design of a large racetrack resonator ..................... 80

Figure 4.16 Simulated optical spectra of a large racetrack resonator showing transmission at the drop port and the through port (in dB) ........................ 81

Figure 4.17 A general schematic of the circuit simulation setup in the Lumerical Interconnect showing 4 different configurations........................................ 82

Figure 4.18 Plot showing ER (in dB scale) vs. detuning (Δλ) for configuration (3) ............................................................................................................... 83

Figure 4.19 Graph showing pulse amplitude from the laser (red line) and the comparison of pulse amplitudes after the propagation through ring filter for lower ER (blue dashed line) and higher ER (black dashed line) obtained .............................................................................................. 83

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Figure 4.20 Power spectrum as a function of frequency (THz) showing adiabatic chirp ............................................................................................................ 84

Figure 4.21 Measured spectra showing the transmission at the through and the drop port for a large racetrack resonator .................................................... 85

Figure 4.22 SEM image of a directional coupler of a fabricated large RR ................... 86

Figure 4.23 Normalized transmission spectra (in dB) showing the simulated and the measured through port response ........................................................... 86

LIST OF ABREVIATIONS AND ACRONYMS

2.5D 2.5 dimensional 2D Two dimensional 3D Three dimensional BOX Buried oxide CMC Certified management consultant CML Chirp managed laser CMOS Complementary metal-oxide semiconductor CMT Coupled mode theory DBR Distributed Bragg reflector DC Directional coupler DCM Dispersion-compensation module DML Directly modulated laser DRIE Dry-reactive ion-etching DWDM Dense wavelength division multiplexing ECL External cavity laser ECR-CVD Electron cyclotron resonance plasma enhanced chemical vapor deposition EM Electro-magnetic EME Eigen mode expansion EML Externally modulated lasers ER Extinction ratio F Fineese

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FDE Finite difference element FDTD Finite difference time domain FP Fabrey-Perot FSR Free spectral range FWHM Full width at half maximum GaInAsP Gallium indium arsenic phosphide Gbps Giga bits per second GHz Giga Hertz HMDS Hexamethyldisilazane ICP Inductively coupled plasma IME Institute of microelectronics InP Indium phosphide INRS National institute of scientific research IR Infra-red ITU International telecommunication union LiNbO3 Lithium niobate LPCVD Low pressure chemical vapor deposition LSCVD Liquid source chemical vapor deposition MDM Mode division multiplexing MEMS Micro-electro-mechanical-systems MRR Micro ring-resonator MZI Mach-Zhender interferometer NGPON2 Next generation passive optical network stage 2

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OSA Optical spectrum analyser OSR Optical spectrum reshaper PDK Process design kit PECVD Plasma enhanced chemical vapor deposition PMD Physical media dependent PMMA Polymethyl methacrylate PON Passive optical network RIE Reactive ion etching RR Racetrack resonator RR Ring-resonator SHREC Silicon photonic hybrid ring-filter external cavity Si Silicon Si3N4 Silicon nitride SiN Silicon nitride SiO2 Silicon dioxide SiON Silicon oxynitride SOI Silicon-on-insulator TE Transverse electric TM Transverse magnetic TWDM Time and wavelength division multiplexing TWR Travelling wave resonators UQAM Université de Québec a Montréal

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varFDTD Variational FDTD WDM Wavelength division multiplexing WGM Whispering gallery modes

LIST OF SYMBOLS AND UNITS OF MEASUREMENT kW Kilowatt Gb/s Gigabit per second Km Kilometers GHz Giga Hertz THz Tera Hertz Λ Grating periods λr Resonant wavelength R Ring radius m Integer number neff Effective refractive index of the waveguide ng Group index of the waveguide n effective index of material C Coupling coefficient κ Field coupling coefficient π pi=3.14 n1 effective refractive index of symmetric mode n2 effective refractive index of antisymmetric mode Δn difference between symmetric and antisymmetric mode λ Wavelength β1 Propagation constant of symmetric mode β2 Propagation constant of antisymmetric mode L Length of directional coupler

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Po Input optical power Pcross Power coupled across the directional coupler t Transmission coefficient Pthrough Power remaining in through waveguide Lx Cross-over length Lc Coupling length g Gap Et1 Through port waveguide mode amplitude Et2 Drop port waveguide mode amplitude α Loss coefficient of the ring |t| Coupling losses of the ring φt Phase of the coupler θ Phase of the ring Pt1 Modal power coming out of the through waveguide Pt2 Modal power coming out of the drop waveguide Pi2 Circulating power inside the ring φ Phase difference variation in-between t and κ in both couplers of ring resonator Δλ Distance between the resonance peaks or FSR 2δλ 3-dB bandwidth EIN(z) Input node ET(Z) Through port node ED(Z) Drop port node

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H Network function relating an input to an output port Ti Gain (or transmittance) of the i-th forward path from an input to an output port. n Total number of ports. Δi Determinant Q Quality factor λ0 Central resonant wavelength dB Decibel mW Miliwatt oC Degree celcius mm Mili meters nm Nano meters μm Micro meter cm Centi meter dBm Decibel-milliwatts dB/cm Decibels per centimetre dB/m Decibels per meter m Meters Qc Quality factor of the coupling between the microdisk and bus waveguide.

(3 Third order non-linear susceptibility pm Picometer ωinst Instantaneous frequency Ith Threshold current

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Symbols for Cascaded Ring Reflector L1 Optical path length of racetrack-resonator 1 L2 Optical path length of racetrack-resonator 2 L3 Optical path length of racetrack-resonator 3 C1 Coupling region formed by bus waveguide and racetrack 1 C2 Coupling region formed by racetrack 1 and 2 C3 Coupling region formed by racetrack 2 and 3 C4 Coupling region formed by bus waveguide and racetrack 4 FSRextended Extended FSR obtained on cascading racetrack resonators m1 Resonant number and co-prime integer of ring 1 m2 Resonant number and co-prime integer of ring 2 m3 Resonant number and co-prime integer of ring 3

INTRODUCTION

With the increasing demand for high data transfer rates, there is a need for high performance

networks that can maximise these transfer rates. Various optical components are being used to

develop wavelength selective mechanisms for lasers and add-drop multiplexers in dense-

wavelength-division-multiplexing (DWDM) optical communication systems. DWDM optical

access networks allow the same spectral efficiency in the last mile as found in the core

networks (Yoffe, Nguyen, Heanue, & Pezeshki, 2012). In order to achieve such high data

transfer systems, the key technology is to implement tunable transceivers including compact,

cost-effective and efficient tunable lasers and optical filters. These efficient and compact

devices can come to a reality by using optical filters such as microring resonators and

microdisk resonators which are already showing an unprecedented reduction in the footprint

of optical devices.(Meindl, 2003)

As advancements in the microelectronic industry increases rapidly, complementary-metal-

oxide-semiconductor (CMOS) compatible photonics tends to overpower the electronic

communication system, since, the data transmission via optical fibres and optical waveguides

system enhances the transmission range and the bandwidth of signals. The benefits of signal

transmission through an optical waveguide are low power consumption, durability and very

low transmission losses in comparison to the traditional electrical transmission lines. With

silicon based integrated photonics, the bandwidths of orders of magnitude larger than the

electronic networks are achievable. Wavelength-division-multiplexing (WDM) enables a

single waveguide to carry multiple data streams. The CMOS compatible photonics allows to

create complex optical devices at the chip scale. Ring-resonators are the prime examples of

compact and high Q-factor filters being widely used in tunable lasers. With this vision, we

present ring-resonator passive optical filters in Chapter 3 to be used as the reflector filters in

the external cavity lasers (ECLs). These have a wide free spectral range (FSR) so as to cover

the entire spectrum of the gain chip, thus, finding its utility in tunable laser applications.

2

The International Telecommunication Union (ITU) requirements for a passive optical network

(PON) systems with a nominal aggregate capacity of 40 Gb/s in the downstream direction and

10 Gb/s in the upstream direction is referred to as the next generation passive optical network

stage 2 (NGPON2). The ITU-T G.989.2 recommendation describes a network supporting

multiple services with bandwidth requirements running at a downstream rate of 4 x 10 Gb/s.

This recommendation based on time and wavelength division multiplexing (TWDM) was

proposed to address the increasing bandwidth demand (Kazovsky, Shaw, Gutierrez, Cheng, &

Wong, 2007). This advancement in the technology compels the development of novel 10 Gb/s-

transmitters which necessitate innovative but also cost-effective and compact solutions

providing long transmission range (>60 Km) and high extinction ratio. Chirp managed laser

(CML) are systems using an external filter in front of a directly modulated laser (DML) to

attenuate the inherent chirp of a laser by aligning the laser wavelength to the transmission edge

of the filter. This allows to significantly increase the extinction ratio and the reach of the signals

by attenuating the data bits ‘0’ and allowing only data bits ‘1’. Thus, in chapter 4, we discuss

and demonstrate a Si3N4 waveguide based compact passive ring resonator, which can be used

as an external filter aiding to increase the extinction ratio of tunable lasers. We present a cost-

effective method to develop such a filter by using the traditional CMOS compatible fabrication

process and its compactness allows the smaller footprint on the chip-scale integration as

compared to other bulky etalon filters.

CHAPTER 1

SILICON PHOTONICS IN OPTICAL COMMUNICATIONS

In accordance with the more than Moore principle, several functionalities have been added at

the chip scale, making them applicable in the diverse fields. The enormous amount of data

storing computers and their associated components deployed within data centres consume large

amount of electrical energy thereby increasing the operation cost. The future of computer

technology rellies on ultra-fast data transfer rates between and within the microchips (Meindl,

2003). The speed of the top 500 supercomputers has increased exponentially during the last

two decades, as shown in Figure 1.1, which is soon expected to reach the Exascale (1018

FLOPs) by year 2020. This increase in the speed is giving rise to huge bandwidth demands,

which according to leading companies such as IBM and Intel, can only be met by investing

Figure 1.1 Performance of the top 500 supercomputers in the world Taken from (https://www.nextplatform.com/2015/07/13/top-500-supercomputer-list-reflects-

shifting-state-of-global-hpc-trends/)

4

heavily in the field of silicon photonics to provide much faster data transfer rates. Thus, silicon

photonics helps in keeping on track with Moore’s Law.

A data centre with many servers incurs high opearational costs and power consumption due to

increase of optical components on a small chip size. Thus, there is a tremendous need for

developing highly efficient miniaturized optical components that could bring down the cost of

high speed optical interconnects to 1$/Gbps. Resolving these challenges need the development

of compact and efficient tunable transcievers which can be used in dense wavelength division

multiplexing (DWDM) systems. These DWDM optical communication systems provides high

performance networks which are able to meet with the high data transfer rates and provide the

same spectral efficiency till the last mile (end users) as it is found in the core networks. High

refractive index contrast waveguides, which can be implemented with the CMOS fabrication

technology, have allowed the development of photonic circuitry using electronic fabrication

facilities. This has made the silicon nitride/silicon photonics one of the most promising optical

integration platforms over the last few years leading to the possibility of developing highly

efficient miniaturized optical components and tunable lasers that could bring down the cost of

optical interconnects.

1.1 Thesis Objective

The main objective of this thesis is to design, fabricate and characterize the silicon nitride

(Si3N4) waveguide based integrated optical filter components with potential application for

wavelength selective devices. A 3rd order Si3N4 ring filter in a reflector configuration will be

designed to have a wide free spectral range (FSR), which can be used to develop a wavelength

channel selection mechanism in a tunable external cavity laser (ECL). This small ring reflector

will provide an optical feedback mechanism and allow the wavelength tuning of a laser. Also,

a Si3N4 ring filter with an aim of developing an optical eye reshaper, will be designed having

a large extinction ratio (ER) to be potentially used as a tunable transmitter in the NG-PON2

systems. This external ring filter having a FSR of 100 GHz, will be used in future along with

the tunable laser to implement a CML. With this view, the optical components such as micro-

5

ring/racetrack resonators will be designed and optimized leading to the innovative transceivers

application.

1.2 Methodology

The devices demonstrated in this thesis were fabricated using a CMOS compatible process.

The research methodology is illustrated in Figure 1.2. The research methodology cycle begins

with an idea emerging through the literature review, brain storming and

workshops/conferences. The design model is based on the standard 8’ Si wafer covered with a

4 μm thick oxide layer. Later, simulations and optimization of basic building blocks such as

directional couplers, Y-splitters, and waveguide bends, are done using analytical models,

further leading to the design optimization of the final devices such as racetrack resonators with

Figure 1.2 Research cycle

6

the aid of the numerical tools such as Eigen-mode expansion (EME) and the finite difference

time domain (FDTD) solvers. Afterwards, the photolithographic mask used for fabrication is

designed. In order to build our devices, we have used the fab facilities of IME*Singapore

accessed via CMC Microsystems (strictly following the PDK) and several other lab facilities

of universities across Montreal, Canada such as INRS, Polytechnic and McGill. The recipes

associated with the microfabrication steps such as dry reactive ion-etching (DRIE), e-beam

lithography, low-pressure chemical vapour deposition (LPCVD) and plasma enhanced

chemical vapour deposition (PECVD) were modified to obtain an optimized process flow in

collaboration with the fellow researchers and the clean room personals. Through the efficient

mix and match of the lithographic techniques, a large range of dimensional issues were

addressed as and when required. After receiving the fabricated chips from the fabs, optical

testing and measurements are performed in the UQAM lab facilities using an advanced

alignment setup to investigate the propagation and insertion losses, followed by the

transmitted/reflected spectrum analysis using an optical spectrum analyser. After this, the data

processing and analysis is done by comparing the simulated and the experimental results,

leading to the model verification and improvement. Eventually the results obtained are

presented in conference presentation. The above methodology cycle was repeated in order to

build each device and some fab-variations were carried out from time-to-time in order to

resolve the structural discrepancies and to solve the challenges arising while testing of the

optical devices.

1.3 Thesis Contributions

In this thesis, we present ring filters in different configurations, contributing to the field of

silicon/silicon nitride photonics as follows:

1) Racetrack resonator filters for CML: We design and demonstrate a Si3N4 racetrack

resonator, with a FSR in close proximity to the ITU channel grid, to be used as an

external filter along with a tunable laser to implement chirp managed lasers (CML).

2) Ring reflector filter for tunable laser: We designed a 3rd order ring filter in a reflector

configuration on a Si platform giving a FSR wide enough to cover the entire C- or L-

7

band. Also, we demonstrate a Si3N4 ring reflector, providing a novel approach towards

future designing of a high order ring reflector (using Si3N4 waveguide), for the tunable

laser application.

1.4 Thesis Organization

This thesis is organized as follows:

In Chapter 2, the state-of-the-art is presented for the silicon (Si)/silicon nitride (SiN) microring

resonator and micro-disk resonator optical filters depicting its advantages over other passive

filters with applications in optical transceivers. In Chapter 3, we present a novel silicon ring

reflector, composed of three racetrack resonators (RRs) coupled in series, in order to have a

wide FSR achieved by the Vernier effect. Also, a single ring reflector based on a silicon nitride

waveguide is modeled and demonstrated. The design and modelling of a single and a cascaded

ring-reflector is carried out using an analytical approach and the obtained simulated results

investigate the important parameters such as the FSR, quality factor, bus-resonator coupling,

ER and transverse modes. Moreover, the transmission and the reflection properties obtained

from the experimental results for a silicon nitride waveguide based single ring reflector

validates the characteristics mentioned above and also the structural discrepancy between the

fabricated and simulated designs. Chapter 4 demonstrates two designs of the SiN waveguide-

based racetrack resonators, to be used in CML. Design 1 is a 4-port add-drop racetrack

resonator having an optical path length corresponding to a FSR of 718.75 GHz, whereas,

design 2 comprises a large optical path length for a specific application in the next generation

passive optical networks (NGPON2) systems. An analytical model, starting from the

directional coupler and leading to the design approach of a fully optimized 4-port add-drop

ring filter is presented. Important characteristics of RRs such as propagating modes, quality

factor, ER, FSR and bus-resonator coupling are investigated in experimental and numerical

simulations.

CHAPTER 2

PASSIVE OPTICAL FILTERS: A LITERATURE REVIEW

Complex photonic integrated circuits are usually constructed from various fundamental

photonic building blocks or components. Fibre Bragg gratings were used early in wavelength

filtering mechanisms because of their flexible filtering capability, low insertion and reflection

losses and low cost. Fibre Bragg gratings were first presented by (Kawasaki, Hill, Johnson, &

Fujii, 1978). Later Lam and Garside in 1981 showed that the refractive index modification was

related to the square of the Argon laser intensity (Lam & Garside, 1981) in the experiments

performed by (Kawasaki et al., 1978). The integration of waveguide Bragg gratings in the

silicon-on-insulator (SOI) platform (G. Jiang et al., 2011; X. Wang et al., 2012) has been of

great interest and its compatibility with the CMOS technology (X. Wang et al., 2012) has made

it even more economically viable providing an ease of fabrication. Thus, they have found

numerous applications in the area of optical communication (Vargas & Vazquez, 2014), such

as WDM filters (Painchaud, Paquet, & Guy, 2007), single channel-extraction filter for dense

wavelength division multiplexing (DWDM) applications (Alonso-Ramos et al., 2014),

dispersion engineering (Cliche et al., 2007), lasers (Rochette, Guy, LaRochelle, Lauzon, &

Trepanier, 1999), optical signal processing (Wang & Yao, 2013), wavelength selection

mechanism and dispersion compensation (Giuntoni et al., 2010) and bio-sensing system

(Jugessur, Dou, Aitchison, De La Rue, & Gnan, 2009). The issues with using Bragg gratings

is that they require a large on-chip area and need an optical circulator to access the reflected

Bragg wavelength signal which adds to the loss in power intensity of the signal. Depending

upon the application, the number of grating periods (Λ) is selected to have an efficient optical

filter. Each grating period has a length of hundreds of nanometres and depending upon

application, the number of grating periods are chosen so as to have an optimum Bragg

wavelength and the band rejection. This results in a large device footprint in the range of

millimetres. When these large size filters have to be used in an active state such as in lasers

and phase-shifted modulators, they need to be thermally or electrically tuned thereby

increasing power consumption (as the whole grating or corrugated area needs to be actuated)

10

and fabrication cost. Therefore, with an increasing demand for optical filters in

telecommunication applications, there is a tremendous need to make compact and

economically viable optical devices in addition to maintaining the high quality factor and

efficient wavelength filtering mechanism. This is provided by micro-ring resonator

(MRR)/microdisk resonators which show a tremendous reduction in the footprint, better

flexibility, less losses and minimal cost. Moreover, the wavelength tuning mechanism for the

wavelength selection process will be electrostatic actuation which needs low power

consumption. Thus, in this chapter, an extensive review of micro ring-resonator and micro-

disk resonator filters is presented illustrating its applicability and leading edge over other

filters.

2.1 Microring Resonators for Transceiver Applications

Passive silicon waveguide structures have shown an unprecedented reduction in the footprint

of wavelength selective devices where microring resonator is a prime and interesting example

of this. A microring is a circular waveguide excited by a bus waveguide where a fraction of input

power from the bus waveguide couples into the ring. The most common coupling mechanism used

is co-directional evanescent coupling between the ring and an adjacent bus waveguide. Resonance

occurs within the ring cavity when the optical path length of the resonator is exactly a whole

number of the wavelengths i.e. for the light whose phase change after each full trip around the ring

is an integer multiple of 2π, which is of course the condition for the light in the ring to be in-phase

with the incoming light from the bus and causes constructive interference. Light which does not

meet this resonant condition is transmitted through the bus waveguide. The expression for the

resonant wavelength is very similar to a Fabry-Perot (FP) cavity and is given by (Bogaerts et al.,

2012):

= (2.1)

where, ‘R’ is the ring radius, ‘m’ is an integer and is the effective refractive index of the

waveguide. In order to achieve an effective ring-resonator, the design of a proper coupling

11

region is required. In the case of a racetrack resonator, directional couplers (DC) should be

studied and designed properly. A DC is the most common device to split and to combine light

in a photonic system. A DC consists of two parallel waveguides where the field coupling

coefficient ‘κ’ is controlled by the coupler gap i.e. the spacing between the two waveguides

and the coupler length. At first, the coupling coefficient ‘C’ is determined using the

supermodes analysis method, based on the numerical calculation of the effective indices n1 and

n2, of the first two eigenmodes of the coupled waveguides. These two modes are known as

symmetric and antisymmetric modes, also generally known as supermodes. The Eigen mode

expansion method (EME) is an another method which is more accurate than the traditional

coupled mode theory (CMT) method (Yariv, 2000) especially for the high-index contrast

waveguides where the coupling coefficient is found using the perturbation methods. From

these two supermodes, the ‘C’ can be written as (Chrostowski & Hochberg, 2015):

= (2.2)

where Δn is the difference between the effective indices, n1-n2, also known as birefringence.

The two modes propagating inside the waveguides have different propagation constants as

given in (Chrostowski & Hochberg, 2015, p. 93):

= (2.3)

= (2.4)

Then a fraction of the power coupled from one waveguide to another can be expressed as

shown in (Chrostowski & Hochberg, 2015, p. 92):

κ2 = = ( . ) (2.5)

where P0 is the input optical power, Pcross is the power coupled across the directional coupler,

L is the length of the coupler and C is the coupling coefficient. Then the remaining fractional

12

power in the original ‘through’ waveguide (assuming a lossless coupler i.e. κ2 + t2 = 1) is given

by (Chrostowski & Hochberg, 2015, p. 92):

t2 = = ( . ) (2.6)

As the modes propagate, the field intensity oscillates between two waveguides as shown in

Figure 2.1, where if the two modes are in phase then the power is localized in the first

waveguide. After a π phase shift difference between the modes, the power becomes localized

in the second waveguide which occurs after a distance known as the cross-over length ‘Lx’

which is shown in (Chrostowski & Hochberg, 2015, p. 93):

β1Lx – β2Lx = π − =

= (2.7)

Figure 2.1 Field propagation along a directional coupler. Modes calculated using the waveguide mode solver and the modes are propagated using the eigenmode

Taken from Chrostowski & Hochberg (2015, p. 95)

The C has a dependence on the distance between the waveguide ‘g’ which follows an

exponential behaviour given by (Chrostowski & Hochberg, 2015, p. 94):

C = B. . (2.8)

13

where A and B are dependent on the geometry of the coupler, optical wavelength, etc. Thus the

field coupling coefficient ‘κ’ can be found for a directional coupler of any length or a gap using

equation (2.5) as shown in (Chrostowski & Hochberg, 2015, p. 95):

= / = sin . = sin . (2.9)

Thus, deciding an optimum value of field coupling coefficient ‘κ’ helps in determining the

important parameters such as gap and coupling length for a directional coupler which is key in

designing complex passive filters. Two types of ring filter configurations are shown in Figure

2.2, where the basic coupling model of a notch filter (Figure. 2.2(a)) and 4-port add-drop filter

(Figure. 2.2(b)) is presented.

(a) (b)

Figure 2.2 Model of a (a) single ring resonator with one waveguide, which forms a ‘notch filter’ and (b) the basic add-drop ring resonator filter

Taken from Rabus (2007, p. 4-7)

For a notch type filter, the coupling between the bus waveguide and the ring is lossless and the

various kinds of losses occurring along the propagation of the light in the ring resonator filter

are incorporated in the attenuation constant. Then the interaction between the bus-waveguide

and the ring can be described by the matrix relation given by (Rabus, 2007):

= − ∗ ∗ (2.10)

14

The complex mode amplitudes ‘E’ are normalized such that their squared magnitude

corresponds to the modal power and the t and k are transmission and field coupling coefficients,

respectively. The * denotes the complex conjugate of t and k. The matrix is symmetric since

the device under consideration is reciprocal. Therefore,

| | + | | = 1 (2.11)

and to further simplify the model, is chosen to be equal to 1. Then the round trip mode

amplitude is given by (Rabus, 2007, p. 4):

= . (2.12)

where, α is the loss coefficient of the ring and θ = ωL/c (for further explanation, please refer

to Appendix I). From (2.10) and (2.12), we obtain the other propagating mode amplitudes

which are presented in (Rabus, 2007, p. 5):

= .∗ (2.13)

= ∗∗ (2.14)

= ∗∗ (2.15)

The corresponding circulating modal power inside the ring is then obtained by squaring the

complex mode amplitudes (i.e. = | | and = | | ), which are derived in Appendix

I. When the loss coefficient α = |t|, then the internal losses are equal to the coupling losses and

the transmitted power becomes zero. This condition is known as critical coupling which is

caused by destructive interference. When, α > |t| then the ring filter is said to be over-coupled

and when α < |t|, it is considered to be under-coupled.

15

Now, when another bus-waveguide is included in the design to make it a 4-port add-drop filter

(as shown in Fig. 2.2(b)), then the mode amplitude at the through port is given by (Rabus,

2007, p. 6):

= ∗∗ ∗ (2.16)

Now the mode amplitude has to pass through the second coupler as can be seen from the Fig.

2.2(b) so as to become the new dropped mode amplitude . The relation for the dropped

mode amplitude in the second waveguide is given by relation presented in (Rabus, 2007, p. 6):

= ∗ / /∗ ∗ (2.17)

where, α1/2 and θ1/2 are the half round trip loss and the phase given by α = / and θ = 2θ1/2.

At the resonance, the output power at the drop port is then given by the square of complex

mode amplitude | |2 (shown in Appendix I). In the case of racetrack resonators, the coupling

distance is approximately the length of the coupling sections. At a point where the curved and

the straight waveguides combine, the mode changes adiabatically between the radial mode of

the curved waveguide and the normal mode in the straight waveguide. Thus, in order to keep

the total optical path length constant, the radius of the curved waveguides should be reduced

if the waveguides are extended. It is important to consider the variation of the phase difference

φ which occurs in the coupling region in both couplers between t and κ. The phase difference

is length dependent and affects the output characteristics, not only in the magnitude but also in

the resonant conditions. This phase difference can be introduced in equations 2.16 and 2.17

using the method described in (Lee et al., 2004) and the complete relation for mode amplitudes

at the through port is then modified to (Rabus, 2007, p. 17):

= ∗ / ( ∗ ∗ )∗ ∗ / (2.18)

16

and at the drop port it changes to (Rabus, 2007, p. 17):

= ∗ / /∗ ∗ (2.19)

The resonant conditions for a racetrack resonator (θ + φt1 + φt2) = 2πm has changed slightly

compared to the ring resonator (θ + φt) = 2πm. The drop port transmission at resonance is no

longer independent of t and κ. Thus, leading to a significant performance change and

confirming the importance of taking into consideration the phase difference.

One important ring resonator parameter is the distance between the resonance peaks, which is

called the free spectral range (FSR) and that can be described by (Rabus, 2007, p. 8):

= Δ = − ≈ (2.20)

If we include the wavelength dependency of the effective refractive index then the group index

ng which is defined as = − , can be included in the equation (2.20). Then the

modified version of eqn. (2.20) given in (Rabus, 2007, p. 9) is:

= Δ = (2.21)

which can be used whenever appropriate to avoid the approximation and hence obtain more

accurate values. Another important parameter is the width of the resonance which is defined

as full width at half maximum (FWHM) or 3-dB bandwidth (2δλ) of the resonance lineshape.

It is derived in Appendix I and is presented in (Rabus, 2007, p. 9) as:

= 2δλ = (2.22)

17

Another parameter that can be directly calculated from the above relations is the finesse (F) of

the ring resonator filter. It is defined as the ratio of the FSR to the width of a resonance for a

specific wavelength (FWHM). This relation is given in (Rabus, 2007, p. 10) as follows:

= = = ≈ (2.23)

One more important parameter which is closely associated to the finesse is the quality factor

(Q) of a resonator which is the measure of the sharpness of the resonant peak. It is defined as

the ratio of the operation wavelength over the resonance width (Rabus, 2007, p. 10) as:

= = = (2.24)

For our design, we have specifically selected three racetrack resonators to be serially coupled

in order to have a reflector configuration. The reflectors can only be designed by choosing the

odd numbers of ring-resonators (such as n=1,3,5,7,…) such as the propagating light is reflected

back to the input port. The coupling of these 3-racetrack resonators will help in achieving a

broad FSR. The representation of the important functional parameters such as field coupling

coefficient (κ), transmission coefficient (t) and the loss coefficient (α) within the ring can be

seen in Figure 2.3. These parameters are kept the same while deriving the transfer equations

for the output ports of the cascaded 3-ring filter. The input node is EIN (z), the through port

node is ET (z) and the drop port node is ED (z). Since there are three rings, there are four

coupling regions in the design. On the basis of the Mason’s rule (Mason, 1956), the transfer

function or input-output transmittance relationship, having ‘n’ number of nodes (16 nodes

depicted in Figure 2.3), from node E1(z) to node En(z) is given by (Chaichuay, Yupapin, &

Saeung, 2009):

= ∑ Δ (2.25)

18

Where H is the network function relating an input to an output port, Ti is the gain (or

transmittance) of the i-th forward path from an input to an output port and n is the total number

of forward paths from an input to an output port. Δi is the determinant Δ after all loops which

touch the Ti path at any node have been eliminated.

Figure 2.3 Model of a serially coupled three-ring add-drop filter showing the coupling coefficients and the loss coefficients for each ring

The forward path transmittances and its determinants from EIN to node ET and EIN to node ED

are shown in Appendix II, leading to the transfer function for the through port as follows

(Chaichuay et al., 2009):

19

( )( ) = =

−1 −1 ( −1) −1 ( −1) ( −1) ( −1)−1 −1 −1 ( −1) ( −1) ( −1) ( −1) (2.26)

Similarly, the transfer function for the drop port is given by (Chaichuay et al., 2009):

( )( ) = = ( ) /( ) ( ) ( ) ( ) (2.27)

In early years, before Si photonics became a path-breaking technology for integrated electro-

optical systems, researchers mainly focused on III-V semiconductors and other glass materials.

The first guided optical ring-resonator was demonstrated by (Weber & Ulrich, 1971) which

was used for a laser application where they presented a device consisting of a 5-mm diameter

glass rod (n=1.47) coated with a rhodamine 6G doped polyurethane film. This coated glass rod

forms a ring like structure, placed in front of the pumping source, providing a positive

feedback. The active medium is provided by the spiral resonator which has a circumference of

31.4 mm. The next relevant demonstration of a low-loss channel waveguides in a ring-

resonator configuration was done by (Haavisto & Pajer, 1980) using a bus-waveguide made of

a doped polymethyl methacrylate (PMMA) film on quartz substrate. Later, the first

demonstration of tunable ring resonator on LiNbO3 with Ti diffused waveguides was made by

(Tietgen, 1984) where they used two 3-dB couplers forming a waveguide loop instead of a

circular ring. This loop has a circumference of 24 mm operating at 790 nm wavelength. The

first ever electro-optically tuned GaInAsP-InP microring notch filter was reported by (Grover

et al., 2004).

Over the past decades, microring resonators have been widely used for implementing a variety

of wavelength-selective reflectors such as reflective notch filters (H. Sun, Chen, & Dalton,

2009) (Shi, Vafaei, Torres, Jaeger, & Chrostowski, 2010) (Chae & Skafidas, 2013) and

reflective band-pass filters (Chung, Kim, & Dagli, 2006) (Paloczi, Scheuer, & Yariv, 2005)

(Poon, Scheuer, & Yariv, 2004). These filters are very promising for applications such as

remote sensing (Shi et al., 2010) (H. Sun et al., 2009), tunable lasers (Sato et al., 2015) (Tao

20

Chu, Fujioka, & Ishizaka, 2009), optical modulators (Xu, Schmidt, Pradhan, & Lipson, 2005),

optical switches (Mokhtari & Baghban, 2015) and WDM add-drop filters (Van, 2007) (W.

Wang et al., 2012) (De Heyn et al., 2013). Over the past two decades, tunable lasers have been

successfully demonstrated on the Si platform since the optical filters made of Si waveguides

provides well confined light propagation. These filters provide a feedback to the laser gain chip

forming a lasing cavity. A general schematic of an external cavity semiconductor laser for

wavelength tuning in telecommunications can be seen in Figure 2.4, where a feedback on one

side of the semiconductor gain element is provided by an optical filter (blazed grating here).

The DBR laser demonstrated by (Y. Liu et al., 2006) is one such example, which has many

attractive performances and is now available for commercial use in optical network systems.

However, for advanced multi-level modulation formats they are hard to use because of their

wider linewidth resulting from their long cavity length.

Figure 2.4 A general schematic of an external cavity semiconductor laser.

This grating has been replaced by compact ring resonators in different configurations such as

a SiON waveguide based serially coupled triple ring-resonator (Matsumoto et al., 2010) in a

loop configuration, in a Littman configuration (Jeon et al., 2008), one with a phase shifter

inside the cavity (Kita, Nemoto, & Yamada, 2014), another with two ring-resonators in series

(R Boeck, Shi, Chrostowski, & Jaeger, 2013) (Ishizaka & Yamazaki, 2006), a polymer

waveguide based single ring reflector using Y-splitters (Paloczi et al., 2005) and in a loop

configuration with an asymmetric Mach-Zhender Interferometer (MZI) (Kita et al., 2014).

Serially coupled two or three ring resonator filters uses the Vernier effect in order to achieve a

wide FSR so as to cover the entire communication C-band. In these configuration, the lasing

21

wavelength corresponds to the simultaneously resonant component with the two/three ring

resonators and is tuned by shifting the resonant wavelengths either by heating one, both (T

Chu, Fujioka, Tokushima, Nakamura, & Ishizaka, 2010) (Ren et al., 2016) or all three ring

resonators (Matsumoto et al., 2010). Other research groups have reported interesting

configurations such as the combination of a microring with a contra directional-coupler

(contra-DCs) (Robert Boeck, Caverley, Chrostowski, & Jaeger, 2015) and integrating a

distributed Bragg reflector (DBR) inside the microring (Arbabi, Kang, Lu, Chow, & Goddard,

2011). This integration was done in order to eliminate the FSR so as to achieve low-threshold

and narrow linewidth single mode laser diodes. This miniaturized half-ring DBR, shown in

Figure 2.5, acts as a narrowband on-chip mirror which is way more attractive than conventional

Figure 2.5 a) Schematic of the ring with integrated DBR. The DBR is realized

by modulating the top half of the ring waveguide. b) SEM image of the fabricated device prior to top cladding deposition

Taken from Arbabi et al. (2011)

DBR because of their small sizes and smooth narrowband high reflective peak at a single

wavelength. In comparison to these configurations, where they have used a waveguide loop as

a reflector within the optical coupling section, we present a novel serially coupled three ring

filter in a reflector configuration where the 3rd order ring filter is integrated with the Y-splitters

and combiners. Moreover, the tuning mechanism used in above mentioned configurations is

thermal (using heaters) which sometimes produces excess heat thereby, degrading the device

performance. In addition to this drawback, they have high power consumption due to thermal

tuning which can be mitigated by adopting an electro-mechanical tuning. Therefore, with the

vision of reducing the power consumption, the ring reflectors presented in this thesis will be

tuned electro-mechanically using micro-electro-mechanical-systems (MEMS) in the future.

22

Another challenge with the silicon waveguide optical filters is the large propagation losses that

degrade the transmission characteristics of the tunable ring resonators. The waveguide

propagation losses reported by (Bogaerts et al., 2012) for silicon waveguides with air cladding

in the IMEC foundry (Selvaraja et al., 2009) was around 2.7 dB/cm resulting in a Q-factor for

an add-drop resonator of 1.36 x 105 for a total length of 13 mm. This was drastically brought

down to around 0.5 dB/cm by (Sato et al., 2015). They reported the best ever output power

with more than 100 mW (20 dBm) at 250C for a silicon photonic hybrid ring-filter external

cavity (SHREC) wavelength tunable laser. This power was high in comparison to the previous

best reported by (Wakaba et al., 2013) of around 90 mW at 700C while achieving a wide tuning

range of around 65 nm. The Si3N4 waveguide is less sensitive to fab dimensions and thus show

low propagation losses as compared to the Si waveguide. Therefore, in this thesis, we

demonstrate Si3N4 waveguide based ring-resonators to be used for different applications. A

novel single ring reflector (similar to (Paloczi et al., 2005)) based on a Si3N4 waveguide and a

Si 3rd order ring reflector design is presented in Chapter 3 with the goal to achieve a wide FSR

with an aid of exploring the Vernier effect such that only a single channel lases within the gain

bandwidth region. Thus, microring resonators are promising integrated filter components for

developing compact external laser cavity allowing wide wavelength tuning range and high-Q

factors at a low-cost for DWDM applications within the telecommunication bandwidth.

2.2 Microdisk Resonators for Transceiver Applications

Microdisk resonator is also a type of ring resonator, also known as travelling wave resonators

(TWR), with a smaller internal radius of the inner ring (can be assumed as two concentric

rings). The main advantage of TWRs over other optical filters such as Bragg gratings lies in the

miniaturization of the devices. For a long time, it has been considered as a key opto-electronic

filter with some of its modes giving a very high Q-factor (Levi et al., 1992). These modes, also

known as whispering gallery modes (WGM), have light circulating around the circumference

of the disk trapped by total internal reflection. In comparison to microrings, microdisks have

smaller footprint, higher Q and wider FSRs which was shown by (Soltani, Li, Yegnanarayanan, &

Adibi, 2010) by developing ultimate miniaturized microdisks and microdonuts (intermediate

design between a disk and a ring shape). Microdisk have unique multi-modal and intrinsic ultra-

23

high Q properties (Soltani, Yegnanarayanan, & Adibi, 2007) due to which, careful coupling

optimization is necessary to extract a single mode with the required Qc (quality factor of the

coupling between the microdisk resonator and bus waveguide). The energy tail of the WGM

of a microdisk decays more rapidly in the radial direction and outside the disk, as compared to

a microring of the same radius. This leads to a weaker coupling of the microdisk to an adjacent

waveguide, compared to the microring, thereby, making it difficult to achieve a critical

coupling. If microdisks have larger radii then achieving the required Qc becomes more

challenging, since the energy tail outside the disk approaches zero faster. A 100% energy

transfer is possible from a bus waveguide to the resonator by an appropriate design of the

waveguide-resonator coupling (Yariv, 2000). A few of the challenges faced when realizing

such compact microdisk resonators are: firstly, the sidewall roughness induces scattering and

absorption losses which can be reduced by developing improved fabrication techniques.

Secondly, optimizing the waveguide-resonator coupling region to achieve critical coupling.

These challenges were analysed by (Soltani et al., 2007) where they demonstrated a high

Q~3x106 Si microdisk resonator. They developed two device architectures for disk-on-

substrate and assessed its integration with active components evidencing the useful role of the

substrate for both chip-scale device integration as well as active electronic device integration.

In order to obtain a directional output, the rotational symmetry needs to be broken which can

be done either by deforming the boundary which gives very low Q-factor (Gmachl et al., 1998),

by inserting a linear defect (Apalkov & Raikh, 2004) or creating a hole (Wiersig & Hentschel,

2006) in a microdisk near the mode propagation region. For a microcavity with a thickness of

only a fraction of mode wavelength, modes can be studied using a 2D approximation with the

help of the effective refractive index n(x, y) = n(r, ϕ). In this approximation, the coordinate

dependence of the EM field in the z-direction is omitted, resulting in the separated fields for

the TM modes (Hz=0) and TE modes (Ez =0). For the TM modes the field is given by the

relation (Dettmann, Morozov, Sieber, & Waalkens, 2008):

+ + + ( , ) = 0 (2.28)

with,

24

=− (2.29) a)

= (2.29) b)

For the TE modes with a new introduced function hz(r,ϕ) = Hz(r,ϕ)/n(r,ϕ), we obtain

(Dettmann et al., 2008):

+ + + (r, ϕ)ℎ + ∇( , ) − 2 ∇( , ) ℎ = 0 (2.30)

with,

= ( , ) + ( , ) ( , ) ℎ (2.31) a)

=− ( , ) + ( , ) ( , ) ℎ (2.31) b)

The relation for the effective refractive index and the field function (ψ) is derived and showed

in Appendix III. Implementation of microdisks on a silicon platform has demonstrated a great

potential for integration with other electronic and photonic devices. Among various micro-

photonic components, microdisk resonators are being actively pursued for chip-scale silicon

photonics (Srinivasan et al., 2005) (Borselli, Johnson, & Painter, 2005) (Johnson, Borselli, &

Painter, 2006). Since, it is the most compact wavelength-selective reflector, it allows highly

competitive tuning efficiency (in nm/W) for tunable lasers (Tao Chu et al., 2009). Due to their

large tuning range and compact size they are promising for other applications such as sensing

(Shi et al., 2012), optical routing switches (Emelett & Soref, 2005), stop-band filters (Morand

et al., 2006), opto-mechanical oscillators (W. C. Jiang, Lu, Zhang, & Lin, 2012; X. Sun, Zhang,

& Tang, 2012), force-gradient-actuated cavity opto-mechanics (X. Jiang, Lin, Rosenberg, Vahala,

& Painter, 2009) (G. Li et al., 2015) and optical modulators (Zhou & Poon, 2006). These micro

resonators have a very long photon life time and a strong electric field enhancement because

of the small mode volumes and a high Q-factor that is achievable at such scale. This makes

them a suitable candidate for the enhancement of light-matter interactions (Barclay, Srinivasan,

Painter, Lev, & Mabuchi, 2006). These optical interconnects tends to revolutionize the computing

technology with a minimal loss and high bandwidths.

25

2.3 Silicon nitride waveguide based Microring and Microdisk Resonators

Over the past decade, we have observed a tremendous development of photonic integrated

circuits over silicon-on-insulator (SOI). The merits of using Si-photonics platform are large-

area substrates, CMOS compatible high yield fabrication, availability of sophisticated

assembly processes and enabling the manufacturing of densely integrated electro-optic

components at low costs and high volumes (Soref, 2006) (Baehr-Jones et al., 2012) (Lim et al.,

2014). Si-photonics is befitting for large complex photonic circuits, optical interconnect

networks and optical switching networks, but, due to the losses, crosstalk and the fabrication

tolerance of the conventional Si photonic platforms, its implementation is sometimes limited.

Recently, low loss Si3N4 waveguide has been considered as a potential candidate for an

integrated photonic platform. Its superior passive optical properties to Si (Henry, Kazarinov,

Lee, Orlowsky, & Katz, 1987), a moderate refractive index (in-between oxide and Si) and low

propagation losses in comparison to Si makes it a suitable material for realizing optical

components for transceiver applications. Si3N4 has other advantages over Si such as it does not

suffer from two photons and free carrier absorption over the telecommunication wavelength

ranges which are preferred for parametric oscillation applications. Moreover, its third order

non-linear susceptibility ( (3)) is about 20 times smaller than that of the silicon (Dinu, Quochi,

& Garcia, 2003) (Ikeda, Saperstein, Alic, & Fainman, 2008). The lower index contrast of a

silicon nitride (SiN, n≈2) to silica (SiO2, n≈1.45) compared to silicon (Si, n≈3.48) reduces

waveguide losses due to sidewall roughness scattering. It is less sensitive to fabrication

variations as compared to Si. Photonic components made of Si3N4 are also less temperature

sensitive owing to a thermo-optic coefficient that is about five times smaller than that of Si

(Amatya et al., 2007) (Cocorullo, Della Corte, & Rendina, 1999). Due to the above mentioned

optical properties, many research groups are currently working and have recently demonstrated

the integration of Si3N4 waveguides onto the SOI platform (Chen, Doerr, Buhl, Baeyens, &

Aroca, 2011) (Jones et al., 2013) (Sodagar, Pourabolghasem, Eftekhar, & Adibi, 2014) and

with hybrid III/V silicon platform (Piels, Bauters, Davenport, Heck, & Bowers, 2014), so as to

combine active and passive optical functionalities in the Si-based integrated photonics.

26

Silicon nitride based waveguides are very promising in an integrated photonics research due

to there CMOS-compatibility (Moss, Morandotti, Gaeta, & Lipson, 2013). Stoichiometric

silicon nitride (Si3N4) deposited using low pressure chemical vapour deposition (LPCVD)

(Epping et al., 2015) offers extremely low intrinsic losses and high reproducibility. It also

provides a broad transparency range from the visible to the mid-infrared region which includes

all the telecommunication bands. The other techniques to deposit Si3N4 are using electron

cyclotron resonance plasma enhanced chemical vapor deposition (ECR-CVD) (do Nascimento

et al., 2014), liquid source chemical vapor deposition (LSCVD) (Cheng, Hong, Spring, &

Yokoyama, 2017) and PECVD (Sacher, Huang, Lo, & Poon, 2015). Some researchers have

demonstrated a very thin ~40 nm Si3N4 waveguides, with weak mode confinement, but

providing ultra-low propagation losses in the C-band of around 0.32 dB/m (Spencer, Bauters,

Heck, & Bowers, 2014). However, this low confinement of the modes has the drawback of

increased bending losses and as a result it limits the density of devices in the integrated circuits.

Ultra-low propagation loss of 0.1 dB/m for low confined Si3N4 waveguides (Bauters et al.,

2011) in comparison to 0.3 dB/m for Si waveguides (Kohtoku, Kominato, Nasu, & Shibata,

2005) have been reported. For highly confined waveguides, the lowest reported loss is around

4.2 dB/m (Luke, Dutt, Poitras, & Lipson, 2013) where scattering losses due to sidewall

roughness are reduced by increasing the thickness of the SiN layer which is low compared to

2-3 dB/cm reported for the standard Si channel waveguide (Lim et al., 2014). The silicon

nitride deposition technique used in our process flow is PECVD (discussed in Chapter 3) which

aids in achieving less lossy waveguide structures.

Thus, silicon nitride waveguides are considered to be a good replacement to silicon waveguides

to fabricate optical devices using a CMOS compatible process. Different optical filters have

been designed but the micro ring-resonator/disk-resonator due to their wide range applicability

are of profound interest. They are being widely used in the telecommunication field for (mode

division multiplexing) MDM-compatible WDM (wavelength division multiplexing)

applications (Yang, Li, Huang, & Poon, 2014), in semiconductor ECL (Oldenbeuving et al.,

2012) (Fan et al., 2014) and as optical add-drop filters (Tien et al., 2011) for channel selection

27

mechanism (Dai, Bauters, & Bowers, 2012). Silicon nitride ring resonators have other

applications in biosensors (Goykhman, Desiatov, & Levy, 2010), in optical coherence

tomography (Yurtsever et al., 2014) in microwave photonics (Marpaung et al., 2013), for lab-

on-a-chip devices due to its compatibility with microfluidic channels (Cai & Poon, 2012)

(Ymeti et al., 2005), for optical parametric oscillator (Levy et al., 2010) and in the visible

wavelength range (Hosseini, Yegnanarayanan, Atabaki, Soltani, & Adibi, 2009) (Stutius &

Streifer, 1977).

MEMS based tunable ring resonators are excellent candidates for wavelength selection in

reconfigurable optical networks due to their static low power consumption and high Q. They

have found application as an optical add-drop filters in reconfigurable optical networks

(Errando-Herranz, Niklaus, Stemme, & Gylfason, 2015), in external cavity tunable lasers (Ren

et al., 2016) and DWDM applications. Different MEMS actuation techniques have been

proposed to perturb the evanescent field of the ring and to extract the resonant wavelength such

as depositing bimorph cantilever on top of ring resonator (Abdulla et al., 2011), by obtaining

a cantilever through etch slots and etch holes (Errando-Herranz et al., 2015), by using comb-

drive actuators (Hah, Bordelon, & Zhang, 2011) (Hah & Bordelon, 2015) and by using micro

mirrors (Brière, Beaulieu, Saidani, Nabki, & Menard, 2015) (Briere et al., 2017). The

deflection of cantilever over the ring resonator resulted in a short wavelength shift of 122 pm

in (Abdulla et al., 2011) as compared to 530 pm of wavelength shift in (Errando-Herranz et al.,

2015). A comb-drive actuation presented in (Hah & Bordelon, 2015) is interesting since the

power is required only during a transition while the resonant wavelength is changed and once

the tuning is complete no more power is required to maintain the tuned state. This tuning is

achieved via evanescent coupling from the resonator to a suspended waveguide (or index

modulator) causing change in the effective indices of the modes propagating through the

resonator. Thus, by varying the distance between the index modulator and the resonator, the

resonant wavelength of the filter can be tuned in a continuous fashion.

Due to the above-mentioned properties and advantages of Si3N4 waveguide devices over

traditional silicon waveguide devices, the passive optical filters based on the silicon nitride

28

waveguides are demonstrated further in this thesis. A reflective optical filter is presented in

chapter 3 which will be integrated along with the MEMS actuating mirrors, as presented by

our team in (Brière et al., 2015), in order to develop a wavelength channel selection mechanism

to implement a tunable laser. By varying the MEMS actuation voltage, the mirror angle can be

changed which helps in selecting one of the ring reflector. This changes the wavelength of the

light that is reflected back inside the gain medium and hence the resonant wavelength of the

laser cavity. The discrete nature of the wavelength selection process simplifies the control of

the electrostatic actuator by enabling a simple feedback mechanism based on a laser output

power. This tunable laser will be implemented along with the Si3N4 racetrack resonator,

presented in chapter 4, to realize a novel tunable transceiver required for long range

transmission of data signal.

.

CHAPTER 3

RING-REFLECTOR FOR TUNABLE LASER APPLICATION

In order to meet the rapid increase in data transfer rates, digital coherent optical communication

system is superseding traditional on-off keying systems. Various optical devices have been

developed for realizing digital coherent systems, such as wavelength tunable laser diode. These

wavelength tunable lasers are expected to have a narrow spectral bandwidth which makes them

an optimum coherent emitter. A tunable laser generally comprises of a gain medium, a lasing

cavity and a wavelength tunable filter. Two types of wavelength tunable filters are presented

in this thesis: a) Serially coupled three ring filter and b) Single ring filter, both in a reflector

configuration which will be micro-mechanically tuned using MEMS actuator in the future. By

changing the voltage, the MEMS actuator changes the mirror angle which helps in obtaining

the lasing wavelength. This can be seen in Figure 3.1, which shows a general schematic of the

micro-electromechanically tuned wavelength tunable laser. The light propagating from the

gain medium is filtered by three ring resonators in the reflector configuration (integrated with

Figure 3.1 A general schematic of a wavelength tunable laser electromechanically tuned using a MEMS actuator

30

Y-splitter/combiner) having different FSRs and is then reflected back to the gain medium

providing a feedback mechanism. These three rings provide a wide FSR by using the Vernier

effect and thus the wavelength channel selection region is wide enough to cover the entire C-

band. Due to the wide FSR, there is only one or two distinctive modal peaks in between the

gain bandwidth region and the wavelength peak with the highest gain lases. Ring reflectors are

chosen, instead of other filters such as Bragg gratings, so as to reduce the footprint of the device

and keep it cost-effective.

Ring filters are the prime candidates to be used in the tunable lasers for WDM applications

(Xia, Rooks, Sekaric, & Vlasov, 2007) (Dong et al., 2010) (Popovic et al., 2007). The

wavelength tuning range has to be wide enough allowing more channels to be utilized in the

WDM systems (R Boeck et al., 2013). Achieving a wide FSR using a single ring is challenging

while maintaining bending losses to minimal and thus several rings are cascaded (Dahlem et

al., 2010) (Popovic et al., 2007) (Xia et al., 2007) in order to have a wide FSR by exploring the

Vernier effect. In the Vernier effect, multiple ring resonators having different optical path

lengths are serially coupled (Fegadolli et al., 2012). Each ring-resonator has a different FSR

corresponding to its total optical path length. When coupled in series, these FSRs gives few

dominant peaks, which are higher than the rest of the peaks in spectrum, showing an alignment

of the resonant wavelengths of the cascaded rings. These dominant peaks represent an extended

FSR. This was shown by (Tao Chu et al., 2009) where for the first time they reported the

wavelength tunable laser module developed with the micro ring-resonators followed by

demonstrating the ultra-wide tuning range of 100 nm (T Chu et al., 2010) next year. They used

thermal wavelength tuning mechanism which causes heat dissipation and consumes high

power which was also used by (X. Li et al., 2015) demonstrating a Si single ring reflector in a

Y-splitter configuration. (Timotijevic et al., 2009) and (Koonath, Indukuri, & Jalali, 2006)

have also demonstrated a wide tuning range on a Si platform but they have showed low

interstitial peak suppression. (Robi Boeck, Jaeger, Rouger, & Chrostowski, 2010) shows a FSR

of 36.2 nm on a SOI platform which is thermally tuned, having a side mode suppression ratio

larger than 11dB. They clearly demonstrated a high interstitial peak suppression of the twin

peaks along with a minimal splitting of the main resonance peak. Other wavelength tuning

31

techniques are opto-mechanical tuning (Ren et al., 2016) and electrical tuning. Few research

groups have demonstrated 3rd order ring filters using Si3N4 waveguide (Barwicz et al., 2006)

reporting a low 3-dB drop loss with a wide FSR of 24 nm (Barwicz et al., 2004). In this chapter

we present a 3rd order and a 1st order reflective ring filters based on silicon and silicon nitride

waveguides, respectively, with an aim of achieving a wide FSR for a wavelength tunable laser

application.

3.1 Design Approach

Our design consists of three racetrack resonators serially coupled and integrated with Y-

splitter/combiner to form a reflector configuration. A schematic of a cascaded 3-ring reflector

can be seen in Figure 3.2 where in all three racetrack resonators have different optical path

lengths (L1, L2 and L3) so as to have different corresponding FSRs. These different FSRs, as

coupled in series, will give dominant peaks showing the alignment of the resonant wavelengths

of the three rings which is due to the Vernier effect. Thus, resulting in an extension of the FSR

that should be large enough to cover the entire C or L band (>40 nm).

Figure 3.2 Schematic of the proposed 3-ring reflector filter having racetrack-resonator serially coupled and integrated with two Y-branch splitters showing propagation

of the reflected and the transmitted light within the filter The racetrack resonators and the Y-splitter/combiner are designed such that, all the resonant

wavelengths (shown by black arrows in Figure 3.2) from the light injected through the input

port are reflected towards the same port. All the non-resonant wavelengths (shown in yellow

32

arrows in Figure 3.2) travel straight towards the through port giving the transmitted peaks. The

waveguide branches of a Y-splitter and a Y-combiner form the bus-waveguides of the rings 1

and 3 and defines a coupling region C1 and C4. The ring 2 forms the coupling regions C2 and

C3 along with the ring 1 and 3, respectively. The Y-splitter/combiner (also known as 3-dB

couplers) are designed such that they split the power equally (50:50) into the two waveguide

branches forming the bus waveguides. When the light mode is injected from the input port, the

light power splits at the Y-junction. The resonant wavelengths are extracted from the light

propagating at the upper branch of the Y-splitter by coupling into the ring 1 through the

coupling region C1 and propagates in a clockwise direction (black colour light) within the

racetrack resonator 1. All the resonant frequencies are coupled then through the coupling

region C2 and propagates inside the racetrack resonator 2 in an anticlockwise direction (black

colour light). Further, all the resonant wavelengths, couples through C3 and propagates

clockwise (black colour light) within the racetrack 3 and finally moves out of the ring and are

extracted at the reflected port. The extended FSR is related to the FSR of each racetrack

resonator by (Schwelb, 2007) (Chaichuay et al., 2009):

FSRextended = m1 FSR = m2 FSR = m3 FSR (3.1)

Where m1, m2 and m3 are resonant numbers for each racetrack resonator and are all co-prime

integers. Initially the racetrack resonators in the design were chosen to be symmetric i.e. they

had similar coupling lengths and constant gaps between inter-ring coupling regions and the

ring and the bus-waveguide regions (the field coupling coefficient κ was same). But later the

coupling regions were optimized to have proper peak response as discussed in equation 2.26

and the ‘m’ values were carefully chosen to avoid occurrence of twin peaks and to obtain large

interstitial peak suppression.

33

3.2 Simulations and Optimization

3.2.1 Simulation of a channel waveguide

In this chapter, we are presenting a single ring reflector and a cascaded 3-ring reflector based

on silicon nitride (Si3N4) and silicon (Si) waveguides, respectively. The silicon nitride

waveguide has a dimension of 435 nm (width) x 435 nm (height), deposited over Si wafer,

buried in between 4 μm thick silicon dioxide (SiO2) cladding from above and 4 μm from below

whereas the Si waveguide is 440 nm wide and 220 nm high deposited over 2 μm thick clad and

protected by 2 μm thick oxide cladding over it. The Si waveguides are fabricated on a SOI

platform. The waveguide geometries are chosen to ensure single mode propagation for the TE

polarization while still having low propagation losses near 1550 nm. The high refractive index

contrast between Si/Si3N4 and SiO2 enables strong confinement of the optical mode. The

chosen dimensions of Si3N4 waveguide provide a single mode propagation which was required

by our industrial partner AEPONYX.

Assuming an ambient temperature of 300K, the waveguide effective refractive index ‘neff’ (for

both Si and Si3N4 waveguides) were numerically calculated using Eigenmode solver in

Lumerical MODE. When a waveguide is modelled, Maxwell’s equations are then formulated

into a matrix eigenvalue problem which are rigorously solved by an Eigenmode solver, giving

the optical mode profiles and effective refractive index of the waveguide modes. The neff and

the group index ng are wavelength dependent and can be seen in Figure 3.3 and Figure 3.4 for

silicon nitride and silicon waveguides, respectively. In Figure 3.4(c), we observe a sudden drop

in the value of ng near wavelength 1600 nm which could be due to some numerical error. If we

go beyond 1600 nm, it follows a same trend (straight line) as before 1600 nm. The propagation

constant of the guided mode at a single wavelength can be calculated as β=2πneff/λ. Since the

neff is highly dispersive, sometimes we have used the group index ng in our calculations for

predicting the FSRs to be more accurate.

= − (3.2)

34

(a)

(b) (c)

Figure 3.3 (a) Perspective view of Si3N4 channel waveguide with insets showing

the cross-section waveguide geometry and TE mode distribution; (b) Wavelength dependent effective index (c) Wavelength

dependent group index

(a)

35

(b) (c)

Figure 3.4 (a) Perspective view of Si channel waveguide with insets showing the

cross-section waveguide geometry and TE mode distribution; (b) Wavelength dependent effective index; (c) Wavelength dependent group index

The effect of the change in the waveguide width on the neff and ng for the silicon nitride

waveguide and the silicon waveguide can be seen in Figure 3.5 (a) & (b), respectively. This

neff dependence on the waveguide width is helpful in analysing the fabrication sensitivity of

the waveguide and its impact on the device performance.

(a) (b)

Figure 3.5 The effect of waveguide width variation over neff and ng at 1550 nm for

(a) Silicon nitride waveguide (thickness of 435 nm), (b) Silicon waveguide (thickness of 220 nm)

36

3.2.2 Simulation of a Directional Coupler

A directional coupler consists of two identical parallel waveguides with an optimized gap and

a coupling length. The desired coupling coefficient and the transmission coefficient are

obtained on the basis of the supermode analysis, as described in equations (2.5) and (2.6). The

other important parameters of directional couplers are calculated using the same approach as

mentioned in section 2.1. The supermodes for both types of waveguides and there neff

dependence over the coupling gap can be seen in the Figure 3.6. The power behaviour within

a directional coupler can be expressed as a function of the structure of the coupler, position of

the coupler, the coupling coefficients and the power transmission ratio. From Figure 3.6 (b)

we can see that for a Si waveguide based directional coupler, the Δn (difference between first

two super modes) is very low and the supermodes converge around 1000 nm gap. On the other

hand, Δn is still high for the directional coupler based on low refractive index contrast

waveguide (in Figure 3.6 (a)) above 1000 nm gap. The symmetric modes of Si3N4 waveguides

at lower gaps are well confined but antisymmetric modes tend to drift towards oxide layer,

which is not the case for Si waveguide. In our simulations we assume that the coupling between

(a) (b)

Figure 3.6 Symmetric and Antisymmetric modes dependence over the coupling gap at 1550

nm for (a) Si3N4 waveguide (b) Si waveguide; with insets showing supermodes electric field distribution

37

(a) (b)

Figure 3.7 Field coupling coefficient ‘k’ versus coupling gap at 1550 nm for (a) Silicon

nitride waveguide having dimensions 435 nm x 435 nm (L=20 μm), and (b) Silicon waveguide having dimensions 440 nm x 220 nm (L=20 μm)

the straight waveguide and ring is solely due to the coupling between the parallel section of

the coupler and it does not include the bent region of the waveguide. The dependence of κ over

varying coupling gaps for the silicon nitride waveguide and the silicon waveguide can be seen

in Figure 3.7 (a) & (b), respectively. We notice that in Figure 3.7 (b), 20 μm long coupler has

an almost zero coupling for a 100 nm gap. This is because the cross-over length (Lx) is 14.37

μm, hence the light goes through (almost) a complete cycle where (almost) all the power is

returned to the original input waveguide. The field coupling coefficient κ helps in deciding the

coupling condition and is carefully chosen to have a critical coupling condition. The κ further

helps in deciding the other important design parameters such as coupling gap, coupling length,

cross-over length, etc.

3.2.3 Simulation of a Silicon Nitride Ring Reflector

A silicon nitride ring reflector includes a single ring integrated with two Y-splitter/combiner.

A general schematic of which can be seen in Figure 3.8. The mask layout dimension for the

straight and the curved waveguides are 435 nm (width) x 435 nm (height) deposited over 4 μm

SiO2 layer and protected by 4 μm oxide cladding over it. The Si3N4 layer is deposited using

LPCVD technique as per the requirements of the fab team in developing the process flow. The

38

ring radius considered for the design is 35 μm which is selected based on the waveguide

bending loss criterion shown in Figure 3.9 where the optical transmission is defined as a ratio

of the output power versus the input power. This helps in achieving the minimum possible total

optical path length so as to achieve a wide FSR with minimal bending and scattering losses.

The total optical path length for the ring resonator is 220.56 μm and is optimized to target the

wavelength of interest at 1550 nm.

Figure 3.8 General schematic of a single ring reflector based on Si3N4 waveguide with dimensions 435 nm x 435 nm

Figure 3.9 Waveguide bend loss versus radius for 435 nm wide Si3N4 waveguide (in dB scale)

The κ is an important parameter for the selection of the design parameters of an add-drop ring

resonator and to achieve the critical coupling condition. The effect of κ on the drop port peak

intensity and on 3-dB bandwidth of the resonance peak can be seen in Figure 3.10. The

39

optimum κ is chosen to be 0.22 so as to achieve the critical coupling condition with high peak

intensity and a narrow 3-dB bandwidth. Based on κ, other design parameters such as coupling

length (Lc) and the coupling gap between the bus-waveguide and the ring resonator are

determined to be 325 nm and 700 nm, respectively. The waveguide propagation loss

considered while simulating is around 1 dB/cm (Bauters et al., 2011).

Figure 3.10 Effect of field coupling coefficient κ on the drop port peak intensity of an add-drop ring resonator

At a wavelength of 1550 nm, the refractive index considered for Si3N4 and SiO2 is 2.04586

and 1.45, respectively. This value of Si3N4 is taken as an average over the wide wavelength

range using Sellmeier equations. The neff of symmetric and antisymmetric mode for a 435 nm

wide Si3N4 waveguide evaluated using finite difference element (FDE) simulations are 1.5281

and 1.4902, respectively (as seen in the inset of Figure 3.6 (a)) and their corresponding group

indices are 1.8326 and 1.9124, respectively. The supermodes are evaluated using the

Eigenmode solver in Lumerical MODE. The Y-splitters are designed to split the light power

equally (50:50) into the two waveguide branches forming the bus waveguides for the ring such

that the reflected resonant peaks are obtained at the input port. The total transmission loss

obtained for the simulated Y-splitter in 2.5D-FDTD is 0.19 dB. The complete optimized design

of the ring filter, including the ring-resonator integrated with the Y-splitter/combiner, is

simulated using the 2.5D-FDTD solver and the obtained spectral response can be seen in the

Figure 3.11 (a). The obtained FSR is around ~6.2 nm with a central resonant peak at 1549.9

40

nm. The transmission peak shows an extinction ratio of around ~67.72 dB. The plot (b) in

Figure 3.11 represents a zoom in of a resonant peak at 1549.9 nm showing a 3-dB bandwidth

of 0.97 nm giving a Q-factor of 1598. The total insertion loss of the device is calculated to be

0.1 dB.

(a)

(b)

Figure 3.11 (a) Simulated spectral response of a silicon nitride single

ring reflector, (b) zoom in of the resonance peak of the reflection/drop port response

41

3.2.4 Simulation of a Silicon Serially Coupled 3-Ring Reflector: The Vernier Effect

In order to design a silicon waveguide based a serially coupled 3-ring reflector as shown in

Figure 3.2, single racetrack-resonators were designed and simulated initially with the goal to

obtain a wide FSR and a narrow 3-dB bandwidth. Once the small ring resonators are designed

having wide FSR, they are serially coupled and further modified by varying the coupling

coefficients κ in order to achieve the optimized 3rd order ring reflector. The effective refractive

indices and their corresponding group indices for a 440 nm wide and a 220 nm high waveguide

are numerically calculated using the Eigenmode solver in Lumerical MODE. The waveguide

geometry was chosen to ensure the single mode propagation for TE polarization, while still

having low propagation losses. This Si waveguide has a 2 μm thick SiO2 cladding above and

below it. The calculated neff for the symmetric and the antiymmetric modes are 2.3504 and

2.3151 (as seen in Figure 3.6 (b)), respectively and their corresponding ng are 4.2180 and

4.4650, respectively. To have a wide FSR, a minimum optical path length is required and

therefore, small ring radiuses (r) (such as 3.2 μm, 3.6 μm and 4.3 μm) are considered and the

design were simulated in the 2.5D-varFDTD simulator using the parameters which are

presented below in Table 3.1. The total optical path length of ring1, ring2 and ring3

corresponding to ring radiuses 3.2 μm, 3.6 μm and 4.3 μm, respectively are 41.6 μm, 37.2 μm

and 34.7 μm. As seen in the Table 3.1, the coupling coefficient (C) is kept constant along with

Table 3.1 Parameters of different RRs (based on Si waveguide) integrated with Y-splitters

r (μm) Lc (μm) g (μm) C Ring 1 4.3 7.3 0.15 0.145 Ring 2 3.6 7.3 0.15 0.145 Ring 3 3.2 7.3 0.15 0.145

the coupling length (Lc) so as to have symmetrical couplers. The insertion loss of about 2 dB

for the ring resonator (Zhang et al., 2013) and about 0.22 dB for the Y-splitters (Zhang et al.,

2013) were included while performing the initial simulations. These loss values were in

agreement with the simulated values using FDTD solver. The drop port spectra obtained from

the 2.5-D FDTD simulation for each ring and there corresponding FSRs can be seen in the

42

Figure 3.12 over a large wavelength range with a common resonant peak around 1492 nm. The

performance parameters corresponding to each ring are presented in Table 3.2 where the

important attributes such as FSR, extinction ratio, Q-factor and 3-dB bandwidth are

summarized.

Figure 3.12 FSRs for three different ring reflectors, each of them showing a common central wavelength around ~1492 nm

Further, a serially coupled three ring reflector is simulated in a 2.5D-var FDTD solver using

the design parameters mentioned in Table 3.1 The obtained reflection response shown in Figure

3.13 gives a FSR of ~20.6 nm between the adjacent resonant peaks. The obtained spectrum is

not as expected, since the dominant resonant peaks which should show an extended FSR are

not distinctive and also each resonance peak shows splitting. The peak splitting shows three

peaks which is due to the cascading of three rings. The similar type of resonance peak splitting

is observed in (Robi Boeck et al., 2010) but with two peaks, where they have serially coupled

two rings in order to demonstrate 2nd order ring filter.

43

Table 3.2 Attributes obtained for Si waveguide based three different ring reflectors

Ring Type FSR (nm) ER (dB) Q-Factor FWHM (nm) λo (nm) r=4.3 μm 13.33 12.58 1243.75 1.2 1492.6 r=3.6 μm 15 12.58 1148.34 1.3 1492.8 r=3.2 μm 15.57 12.57 1066.5 1.4 1492.9

As discussed in (Robi Boeck et al., 2010), some of the factors must be ensured in order to

achieve the optimized performance such as: (i) the removal of twin resonance peaks located in

between the main resonance peaks, (ii) to make sure that the main resonance peak intensity is

high (i.e. ensuring low insertion loss), (iii) there is a minimal splitting of the main resonance

peak and (iv) there is a large interstitial peak suppression. Thus in order to optimize the device

performance some design parameters were changed. As the total optical path length of the rings

determines the extended FSR, so path lengths were carefully selected. Moreover, the power

coupling factors also need to be optimized to obtain high main resonance peak intensity,

minimal main resonance peak splitting and a large interstitial peak suppression (Schwelb,

2007) (Chaichuay et al., 2009) and thus, the field coupling coefficient ‘κ’, the coupling gap ‘g’

Figure 3.13 The reflection response of a serially coupled 3-ring reflector in a 2.5D-FDTD showing resonance peak splitting

44

and the coupling length ‘Lc’ for each of the ring were changed. The ‘κ’ for three rings was

carefully chosen in order to have a critical coupling and a narrow 3-dB bandwidth using the

analytical equations in MATLAB as shown in Appendix IV. This κ further determines the

design parameters such as g and Lc using parameters in 2.5D-FDTD simulations to accurately

design the ring reflectors. The selected radiuses for the individual ring resonators are 3.6 μm,

10 μm and 4.3 μm. According to equation (3.1), the extended FSR is related to the m (co-prime

integer values) times the FSR of an individual ring and the m values are chosen to be 3, 5 and

7. Three plots in Figure 3.14 shows the effect of κ on the drop port intensity and its 3-dB

bandwidth for three different rings, which is evaluated using the drop port transfer function

equations in MATLAB. The selected parameters based on the optimum κ values are

summarized in Table 3.3.

(a) (b)

45

(c)

Figure 3.14 The effect of the coupling coefficient ‘κ’ on the drop port peak intensity of Si

waveguide based single ring resonator of radius (a) 3.6 μm (b) 4.3 μm and (c) 10 μm

Table 3.3 Optimized design parameters for Si waveguide based three different single ring reflectors

Radius (μm)

Coupling Length (μm)

Gap (μm)

Field Coupling

Coefficient (κ)

Total Path Length of RR

(μm) Ring 1 3.6 2.6 0.15 0.145 27.81 Ring 2 10 1.59 0.18 0.137 66.01 Ring 3 4.3 2.007 0.15 0.145 31.03

The total optical path length of each ring is selected to target the desired resonant wavelength

of 1.55 μm. The coupling length for each ring resonator (RR) is assumed to be of straight

parallel waveguides, excluding the bend region. The total optical path length for each of the

ring resonator is presented in Table 3.3. The Y-splitters are designed to provide a 50:50 power

splitting and are simulated in 2.5D-FDTD. The total transmission loss of the simulated Y-

splitter is 0.17 dB. The reflection spectra for three different rings is shown in Figure 3.15

comparing there FSRs which are quiet high compared to previous designed RR’s (as shown in

Figure 3.12) and are centred around desired wavelength of 1550 nm. It shows high drop port

peak intensities of around 94% of the total input light intensity. The other output performance

46

Figure 3.15 Reflection spectra obtained from 2.5D-FDTD for three different Si ring reflectors showing their corresponding FSRs

Table 3.4 Performance parameters for the optimized single Si ring reflectors

Ring Type FSR (nm)

ER (dB)

Q-factor

FWHM (nm)

λo (nm)

r=3.6μm 25.3 30.09 337 4.59 1550.89 r=10μm 11 19 1409 1.1 1550.07 r=4.3μm 23.52 17.56 500 3.1 1550.07

metrics such as ER, the Q-factor and the FWHM for three different ring reflectors are

summarized in Table 3.4. The spectrum shows a high ER and a wide 3-dB bandwidth but the

Q-factor obtained is low. This could be due to the over-coupling at the coupling region (i.e. κ

< α) which leads to a wider 3-dB bandwidth. Also, the propagation losses and the coupling

losses within the device seems to be high leading to improper coupling which can be seen due

to irregular lower region of the curves. Since, the bend radii selected are also small, to achieve

wide FSR, so the losses due to bends also impacts the spectral peaks and thus the spectral

response is not proper.

47

Finally, a cascaded 3-ring reflector is simulated using the optimized design parameters of three

different ring-reflectors presented above (in Table 3.3) with an aim of achieving an extended

FSR by an aid of exploring the Vernier effect. A quality optical spectrum showing the proper

dominant resonant peaks with an extended FSR, the minimum peaks possible in-between the

dominant resonant peaks and no main resonance peak splitting is expected. The whole structure

is simulated using a 2.5-D variational FDTD mode solver. The obtained optical spectrum from

the reflection port can be seen in Figure 3.16, showing an extended FSR of around 90.2 nm.

We can clearly observe the two distinct dominant resonant peaks at 1428.8 nm and 1519 nm.

Although the targeted wavelength was near 1550 nm but as seen in Figure 3.16 the resonant

wavelengths of the rings have shifted. Also, the interstitial peak suppression is increased to 7.6

Figure 3.16 Reflection spectra for a serially coupled Si 3-ring filter illustrating the Vernier effect and showing the dominant resonant peak without peak splitting

dB in comparison to the previous response of 1.35 dB (in Figure 3.13). The obtained extended

FSR of 90.2 nm is wide enough to cover the entire C or L-band (40 nm) as compared to any of

the single ring reflectors presented above. We can clearly see that the peak splitting for the

dominant resonant peaks has been resolved, as it was done in (Robi Boeck et al., 2010), in

48

comparison to the peaks observed earlier (in Figure 3.13). But the twin peaks still exist

probably because the co-prime integer numbers m1, m2 and m3, as mentioned in equation (3.1),

for this design still need to be improved. To remove the occurrence of the twin peaks, m2 should

be equal to m1-1 (assuming m1 > m2) and m3 should be equal to m2-1 (assuming m2 > m3). If

the integer numbers increase, the interstitial peak suppression decreases and so they need to be

small enough to give an adequate interstitial peak suppression. As the κ < α (as seen in Figure

3.15), the optimization of κ values will lead to a proper and smooth spectral response of an

individual ring giving a narrow 3-db bandwidths. Moreover, in order to decrease the resonant

peak intensities in between the dominant resonant peaks, more optimization need to be done

with respect to carefully choosing the co-prime integer multiple of FSRs and also by optimizing

the κ which will be done in the future.

3.3 Fabrication, Measurements and Analysis

3.3.1. Mask Layout Description

The Si waveguide based cascaded ring reflector could not be fabricated at IME foundry within

the given time frame due to the fab challenges and time constraints since the tools in the

foundry were down for very long period. For the fabrication of a Si3N4 ring reflector, a single

ring resonator is integrated with the Y-splitters, such that the Y-splitter branches form the bus

waveguides as shown in Figure 3.8. The layout for the devices is made in the K-layout

software. The total chip area is 1.5 cm x 2 cm. The mask dimensions for the straight and the

curved waveguides is 435nm (wide) x 435 nm (height). The gap distance between the ring and

the straight bus waveguide is kept at 700 nm and the total optical path length of the ring is

220.56 μm. No grating couplers or tapers are used at the end of the devices, allowing light to

couple directly from the fibre to the waveguide edge facet. Considering fabrication constraints,

few replicas of optimized ring-reflector designs along with the variation in the waveguide

width and the coupling gaps have been incorporated within the chip. In total, there are 14

devices out of which devices 1-7 are the replicas of the final optimized design, designs 8-10

have waveguide width variations and designs 11-14 have varying coupling gaps. These several

49

design variations allow the possibility of achieving at-least one working device with the desired

output spectral response as we expect at least one device to have a desired waveguide

geometry.

3.3.2 Fabrication Process Flow for Si3N4 structures.

The different design variants developed through the simulation models are further processed

for fabrication to understand their limitations and their optical response, using micro-fab

techniques. These devices are fabricated in the various fab- and the clean room facilities across

the Montreal region especially at McGill, Ecole-Polytechnic and National Institute of

Scientific Research (INRS) universities. The SiN devices are deposited over the standard 8-

inch silicon wafer. At first the Si wafer is cleansed using the chemical baths in order to remove

the contaminants which may lead to a poor adhesion or a defect formation in the resist layer.

The first layer deposited over Si substrate is the SiO2 layer acting as a buried oxide (BOX)

layer which is grown thermally. This is followed by the deposition of a SiN layer over a SiO2

which is done using LPCVD technique which deposes Si-rich low stress SiN layer. This is

further covered by the chromium (Cr) hard mask to have easy pattern transferring after dry-

etch as Cr has high resistance to plasma etching. After that, the sample is made ready for the

lithography step by adding an adhesion promoter such as hexamethyldisilazane (HMDS),

which enhances the adhesion of the resist to the substrate. In the next step, a negative tone e-

beam resist such as ma-N-2401 is spin coated over HMDS. Once the sample is ready for

lithography, it is e-beam irradiated causing chemical changes in the exposed area which

influence the solubility of the exposed area relative to the unexposed area of the resist in a

developing solvent, thus leaving behind the SiN patterned structures. Then SiN layer along

with the Cr hard mask and negative e-beam resist are etched using inductively coupled plasma

(ICP) cryogenic reactive-ion-etching (RIE). After this, all of the Cr layer and negative resist

which is left over the waveguide structures is removed leaving behind only SiN waveguides.

Then at last, these waveguides are protected by deposing a SiO2 cladding over the structures

using the PECVD technique. The recipes associated with the microfabrication steps such as

DRIE, e-beam lithography, LPCVD, PECVD, etc. are modified from time to time in order to

50

obtain an optimized process flow in collaboration with the fellow researchers and the clean

room personals. Some of the dimensional issues of the devices have been addressed as and

when needed through the efficient mix and match of the lithographic techniques. A general

process flow for fabricating the Si3N4 waveguide structures over the standard Si wafer

developed at various lab facilities is presented in the Figure 3.17:

Figure 3.17 A generalised process flow for the fabrication of the Si3N4 waveguide structures.

3.3.3 Optical Test Setup

To take the measurements of the fabricated devices a setup with two optical fibres as shown in

the Figure 3.18 (1) is used with the tapered lensed tips pointing towards each other such that

the chip facet and both fibres are aligned at the straight axes without any angle inclination.

Both input and the output fibres are single mode lensed fibre with a mode field diameter of

around 3.3 μm. The TE polarization is maintained for the input mode fibre using a polarization

rotator (shown in figure 3.18 (6)). No grating couplers have been used for the fibre-to-

waveguide coupling. Alignment of the fibres to the waveguide on the chip edge facet is

51

achieved with the help of a triple axis stage controller which is a NnoMaxTS purchased from

the Thorlabs (shown in Figure 3.18 (5)). The chip containing the devices rest over the centre

Figure 3.18 Optical Test Measurement Setup (1) (a) Single mode input fibre (b) Single mode output fibre (2) Device chip (3) Chip holding stage (4) Chip stage controller (5) Three axis stage controller for (a) input fibre (b) output fibre (6) Polarization rotator (7) Microscope

stage and on the other two stages lie the input and the output fibres. Also, the visible and infra-

red cameras are used to achieve alignment via a microscope that is connected to a computer

and are managed by Thorlabs and USB2.0-ARTCAM-008TNIR software, which visually

displays on computer monitor. An optical power meter, of model N7744A purchased from the

KEYSIGHT, is used to measure the optical power (in dBm) which is highly sensitive. A

narrowband tunable laser source (model no.: 8168F) purchased from the KEYSIGHT-Agilent

has a tuning range of 112 nm from 1480 nm to 1592 nm. The output spectra are measured

using an optical spectrum analyzer (OSA), model no.: MS9710B which has a wavelength range

from 0.6-1.75 μm.

52

An Optical Fiber Amplifier (AEDFA-33-B-FA) is used to send a broadband signal through the

devices via an input polarization maintaining fiber. The device response is then measured by

the OSA. The following procedure is followed to measure all the devices:

a) The chip is aligned with the input and the output fibers with the help of a visible and

an IR camera along with the microscope and the three axis stage controllers;

b) Firstly, a broadband signal is sent through the devices and there output spectrum is

measured in the OSA;

c) Once output peaks are observed, then the broadband source is switched by the

narrowband tunable laser source for better accuracy and to obtain sharp peak intensities

with a better resolution;

d) A tunable laser is set to an arbitrary wavelength;

e) Some minor adjustments to the lateral positions of the fibers is done until a maximum

intensity is achieved at the output;

f) Then a sweep across the wavelengths is carried out to measure the maximum output

power via an optical power meter;

3.3.4 Measurements and Analysis

The Si waveguide based cascaded ring reflector was not fabricated due to the fabrication

challenges at the IME foundry and thus were not measured. Out of 14 devices on the chip

containing SiN based ring-reflector designs, data is extracted only for devices 6, 8, and 9

because only 3 devices showed transmission response at the through port. For the remaining

devices the spectral peaks are not observed at the through port nor at the reflected port. The

reason for no output, at either of the ports, for the remaining devices could be due to the

propagation losses within the waveguide, scattering losses due to waveguide surface

roughness, bending losses at the bent junctions in Y-splitters and coupling losses at the

coupling region of the ring and the bus waveguide due to fabrication discrepancies. The

simulated waveguide width for the device 6, 8 and 9 are 435 nm, 445 nm and 455 nm,

respectively. Thus, they are expected to show different peak response as the device output

53

spectrum is sensitive to the fabricated waveguide dimensions and the sidewall roughness. The

measured transmission response for devices 6, 8 and 9 are shown in Figure 3.19 and the

comparison of the transmission response between three devices can be seen in Figure 3.20,

(a) (b)

(c)

Figure 3.19 The through port transmission response for (a) Device 6, (b) Device 8 & (c)

Device 9

which clearly shows a shift in the resonant peaks. For device 6, the observed resonant

wavelength is at 1549.5 nm which is off by 0.5 nm from the targeted wavelength giving an

FSR of ~6.03 nm. This FSR value is 0.17 nm off from the desired value of 6.24 nm. For device

8, the resonant wavelength nearest to the target wavelength is obtained at 1550.58 nm at an

offset of 0.58 nm. The obtained FSR for device 8 is around ~6 nm which is off from the desired

value by 0.24 nm. Similarly, for device 9, the observed resonant wavelength is at 1546.44 nm

which is offset from the targeted wavelength by 3.56 nm. It gives a FSR of ~5.82 nm which is

54

less than the desired value by 0.42 nm. The important attributes obtained from the

measurements characterizing device performance are illustrated in the Table 3.5.

The reflection spectrum is not presented as no response is obtained at the reflected port which

could be due to the coupling losses, waveguide propagation and scattering losses and also the

losses induced due to the circulator which is attached to the input fiber for measuring the

reflection. Due to this reason only the through port response is presented. The comparison

between the theoretical and the experimental transmission response is presented in Figure 3.21

where we can clearly see that the targeted resonant wavelength for the simulated response is

1550 nm. The measured response for the devices are slightly off from the simulated one and

the FSR’s obtained are in close proximity to the theoretical FSR of 6.2 nm. Out of three, device

6 gives the lowest 3-dB bandwidth and thus gives the highest Q-factor. Also the extinction

ratio is around 12.81 dB which is good enough to be used in the DWDM applications. The

device 8 and 9 shows an ER of around 8.5 dB but has a poor Q-factor and a 3-db bandwidth.

The output performance of these measured devices is not very well in accordance with the

simulated designs and we can see some shift in the output metrics. A detailed analysis of the

waveguide dimensional factors leading to such a performance is discussed next. Some other

possibilities could be the inclusion of the lower value of waveguide losses while designing and

simulation leading to the scattering of light and the propagation losses.

Table 3.5 Important attributes illustrating fabricated device performance

Device Type FSR (nm)

ER (dB)

Q-factor

FWHM (nm)

λo (nm)

Device 6 6.03 12.81 1122.82 1.38 1549.5 Device 8 6 8.65 660 2.34 1544.62 Device 9 5.82 8.84 678.26 2.28 1546.44

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Figure 3.20 Comparison of the through port transmission response for 3 devices.

This difference in the FSR could be due to the variation in the expected waveguide

width of 435 nm and the actual waveguide width. A SEM image of other device on the

same chip is shown in Figure 3.22 which presents a top width of 386 nm and the bottom

width of 427 nm with a thickness of 453.6 nm in comparison to the actual 435 nm x

435 nm design. The average width comes out to be 406 nm which is reduced by almost

30 nm from the actual dimension and the thickness has also increased by 5% of the

actual dimension. Moreover, both of the coupling gaps measured are off by

approximately 40 nm which leads to under-coupling. The discrepancy analysis of the

fab dimensions for some devices on the chip shows that the waveguides are over-etched

and is expected to be followed for the rest of the devices on the same chip. The effect

of the fabrication on the device performance can be analysed from the Figure 3.23

which shows normalized curves for three devices having different widths and

comparing their simulated and the experimental response. From the plots in Figure

3.23, we can infer that as the waveguide width increases (435 nm>445 nm>455 nm)

for the devices, their corresponding FSRs decreases (6.03 nm>6 nm>5.82 nm). This

56

(a)

(b)

Figure 3.21 (a) Theoretical vs Experimental through port response for devices 6, 8 and 9 (b) Zoomed in response of plot (a)

57

(a)

(b)

Figure 3.22 SEM image of the (a) fabricated waveguides forming the coupling region and (b)

the cross section of the waveguide.

58

holds true theoretically, since as the waveguide width increases, the effective refractive

index of the waveguide increases (Figure 3.5) and so does the group index and thus the

FSR is expected to decrease (from eqn. 2.20 and 2.21). Also, the resonant wavelength

(or the targeted wavelength) has been shifted to the left (i.e. it has reduced) for all of

the devices as discussed above which holds true theoretically, since λr reduces as the

neff of the waveguide reduces due to the decrease in the waveguide width (eqn. 2.1).

The thickness of the waveguide also plays a major role in guiding the mode propagation

in a confined manner. The waveguide allows guided wave propagation only if the

thickness is greater than the critical cut-off thickness for each waveguide mode. If the

thickness of the waveguide is below the cut-off thickness than the light is no longer

confined in the waveguide and it begins to leak into the substrate. Thus, the thickness

of the waveguide also determines the guiding modes in the waveguide (Gang, 2005)

and is considered to be an important factor in deciding the output performance of the

devices. The thickness of a silicon nitride waveguide used in designing a ring reflector

is optimum for guiding a lowest order TE mode. The cut-off thickness for a three- layer

waveguide structure (nsubs = 1.45, ncore = 2.0458, nclad = 1.45) at a wavelength of 1550

nm is shown in Table 3.6. The cut-off thickness is evaluated using a MATLAB code

shown in Appendix V. For only the lowest order TE mode to propagate inside the

waveguide, the thickness must be less than 537 nm. The thickness of the fabricated

waveguide is approximately ~453 nm and so it is well within the cut-off range of the

first order TE mode. A plot in Figure 3.24 shows the tolerance of the waveguide’s neff

due to the change in the waveguide thickness and the waveguide width for the

fabricated waveguide dimensions.

59

(a) (b)

(c)

Figure 3.23 Normalized curve showing theoretical vs experimental response for varying

widths (a) Device 6 (435 nm) (b) Device 8 (445 nm) (c) Device 9 (455 nm)

Table 3.6 Cut-off thickness for the waveguide structure

TE Modes Cut-off thickness (μm) 0 0 1 0.537 2 1.07 3 1.62 4 2.148 5 2.685

The measured FSR of each device should be higher than the theoretical value since the

waveguide width has reduced (thereby reducing the neff and ng), but that is not the case. This

shows that there are some other factors related to the neff or ng, which plays an important role

60

in deciding the FSR. One of the factors could be the thickness of the waveguide as discussed

in (Gang, 2005). A change in the thickness of the waveguide seems to have more impact on

(a)

(b)

Figure 3.24 The effect on the neff of the fundamental TE and TM mode for the (a) Fabricated

waveguide width (386 μm top x 427 bottom) vs. the varying waveguide thickness and (b) Fabricated waveguide thickness of 453 μm vs. the varying waveguide width.

the device performance as compared to the change in the width of the waveguide which can

be seen from the plots in Figure 3.24. If the waveguide width is kept constant (as fabricated)

61

and the waveguide thickness is varied, then the effect on the neff of fundamental TE and TM

modes can be seen in plot (a) of Figure 3.24. Whereas, the effect on the neff of fundamental TE

and TM mode due to the variation in the width when the thickness is fixed at 453.6 nm can be

seen in plot (b) of Figure 3.24. The linear curve fit of data in both the plots show that the slope

of the TM mode is higher in plot (a) as compared to the slope of the TM mode in plot (b) of

Figure 3.24. Thus, the neff is more sensitive to the change of the waveguide thickness than the

width of the waveguide. To mitigate this fabrication variation, the iterations based on the

simulation and fabrication data will be done in the future, achieving the neff in the close

proximity to the desired one, and thus, giving the desired output performance of the devices.

3.4 Summary

To summarize, we have demonstrated a single ring reflector based on a Si3N4 waveguide. It

uses a racetrack resonator with a 35 μm radius connected to a Y-splitter and a combiner

forming a reflector configuration. One out of three devices, device 6 shows an extinction ratio

of 12.81 dB with the resonant wavelength at 1549.5 nm, which is in close approximation to the

targeted wavelength of 1550 nm. The measured FSR of the fabricated device is 6.03 nm. The

obtained 3-dB bandwidth of the resonant peak is 1.38 nm giving a Q-factor of 1122.82. In

future, a serially coupled 3-ring reflector, based on a silicon nitride waveguide, will be

developed with a target of achieving an extended FSR wide enough to cover the entire C or L-

band spectrum. The other reflector type is a 3-ring reflector cascaded in series, designed using

a silicon waveguide. This ring reflector is theoretically designed showing an extended FSR of

90.2 nm which is wide enough to cover the entire C or L-band (40 nm), in comparison to a

single ring reflector by using Vernier effect. It shows an interstitial peak suppression of 7.6 dB

with no dominant resonance peak splitting. Further, the twin peaks need to be removed by the

careful selection of an integer multiple of FSR (m) and also by choosing the accurate coupling

coefficient κ, which will be done in the future. These devices propose an optical 3rd order ring

filter that is promising for a wavelength channel selection system in a tunable laser, tuned via

MEMS actuator.

CHAPTER 4

RACETRACK RESONATOR FOR THE CHIRPED MODULATED LASER

Over the past decade, there has been a tremendous growth in the data services due to the large

files downloading, online streaming, high definition televisions and massive multiplayer online

games, resulting in the upgradation of the access networks. In the current market, upgrading

the metro systems capacity from 2.5 to 10 Gb/s is the prime interest for most of the carrier

operators, without adding costly dispersion-compensation modules (DCMs). The International

Telecommunication Union (ITU) recommendation ("40-Gigabit-capable passive optical

networks 2 (NG-PON2): Physical media dependent (PMD) layer specification ", 2014)

specifies the physical media dependent (PMD) layer requirements for a passive optical network

(PON) system with a nominal aggregate capacity of 40 Gbit/s in the downstream direction and

10 Gbit/s in the upstream direction, which is referred to as the next generation passive optical

network stage 2 (NG-PON2). NG-PON2 is basically a flexible optical fibre access network

which is capable of supporting the bandwidth requirements of mobile backhaul, business and

residential services. Four (4) x 10 Gb/s time and wavelength division multiplexing (TWDM)

was proposed to address the increasing bandwidth demand as part of the NG-PON2 (Kazovsky

et al., 2007). Due to this advancement in the technology, the 10 Gb/s-transmitters were

developed which necessitates innovative but also cost-effective and compact solutions

providing long reach transmission (>60 Km) and high extinction ratio (>10 dB).

Among the solutions considered for achieving the high extinction ratio (ER) and the long range

transmissions, the externally modulated lasers (EML) is one key example. The other attractive

and widely used candidate is the directly modulated lasers (DML) which is low cost, consumes

low electrical power and provide high output optical power. Although the signal generated

with the direct modulation is considered to be robust as the output power of the device directly

depends on input drive current, but is severely distorted (shown in Figure 4.1) during the fiber

transmission because of the inherent chirp of the DML. At high bit rates, direct modulation

generates frequency chirp that interacts with chromatic dispersion in the fiber thereby limiting

64

the range of the transmission and making it difficult to achieve a high ER. Chirp is the time

dependence of the instantaneous frequency of an optical pulse which basically occurs due to

the change in the refractive index associated with the change in the carrier density (Paschotta).

Up-chirp means that the instantaneous frequency rises with the time, whereas down-chirp

means that the instantaneous frequency decreases with the time. The chirp manifests in

primarily 2 manners when a semiconductor laser is directly modulated: -

a) Chirp which occurs at the bit transitions is known as transient chirp.

b) Chirp that causes ‘1’ bits to blue shift relative to the ‘0’ bits is known as adiabatic chirp.

(a)

(b)

Figure 4.1 (a) Electrical signal at the input, and a distorted (b) optical signal at the

output, of a DML due to chirp

The principle of any semiconductor laser or DML is based on modulating the bias current upto

the threshold value (Ith) to modulate the laser. The increase in the bias current increases the

number of charge carriers in the active region thereby leading to the reduction in the refractive

index which in turn reduces the instantaneous frequency (ωinst). This is known as a positive

chirp or blue shift of ωinst which is on the rising edge. If bias current decreases, then carrier

density decreases thereby increasing the refractive index and thus increasing the ωinst which is

65

known as negative chirp. It is on the falling edge of the frequency (J. Liu & Kobayashi, 2010).

This positive and negative chirp of the frequency can be seen in the following Figure 4.2.

Figure 4.2 Change of instantaneous frequency ωinst with time showing blue and red shift

Some of the solutions to overcome the challenge of chirp are dispersion compensating fiber

(Mizuhara, Nguyen, Tzeng, & Yeates, 1995), spectral broadening reduction (Binder & Kohn,

1994) or electronic dispersion compensation (Feuer, Huang, Woodward, Coskun, &

Boroditsky, 2003) and specific optical filtering (Wedding, 1992) (Morton et al., 1996). Many

directly modulated distributed feedback (DFB) lasers operating at 10 Gb/s have been

demonstrated and being used in the optical fiber and the telecom industry ("40-Gigabit-capable

passive optical networks 2 (NG-PON2): Physical media dependent (PMD) layer specification

", 2014), but they lack the rapid tunability required for the latest NG-PON2 standard. The DFB

lasers required in NG-PON2 will be used in the burst mode for TWDM and point-to-point

WDM. One approach to implement a tunable DML is to design the DBR laser in such a way

that it can be tuned electrically and independently from the laser gain. However, due to the

inherent chirp of the DMLs, the signal reach of the transmitters is limited. In order to mitigate

these problems, chirp managed directly modulated laser (CML) came into existence and are

considered as a breakthrough technology for the rapid tunability required by the NG-PON2.

The CML is an alternative transmitter technology using an external filter in front of the DML

to attenuate the laser signal transmitting data ‘0’ bits and allowing only data ‘1’ bits signals to

pass through, which significantly increases the ER and thereby extending the reach of the

signals.

66

In particular, a CML transmitting over 200 km at 1550 nm was demonstrated (Matsui et al.,

2006) but at the expense of a complex wavelength algorithm to suppress the time dependent

chirp and the use of the relatively bulky etalon filter, which increases the cost. A DFB laser

with a microring resonator (MRR) (Gallet et al., 2016) (Chimot et al., 2016) as an external

filter has been demonstrated. The MRR as an optical filter along with the DFB laser has been

implemented either in silicon photonics (Gallet et al., 2016) or in III-V semiconductor

materials such as indium phosphide (InP) (Chimot et al., 2016). Here, we demonstrate a MRR

made with silicon nitride (SiN) waveguides using a CMOS compatible process as a potential

external filter to be used along with the tunable laser. The tunable laser used for developing

tunable CMLs will have a chirp of 10-30 GHz. The filter type we demonstrate has advantages

such as compactness and cost effectiveness since we use a Si3N4 racetrack resonator. This

optical filter will be used in future as an optical spectrum reshaper (OSR) in order to built a

transmitter for the NG-PON2 channel grid. The low propagation losses of SiN waveguides

enable the implementation of a large but an efficient MRR having a FSR that matches the ITU

(ITU-T G.989.2, 2014) network grid of 100 GHz (0.8 nm) spacing in optical frequency. Thus,

it is possible to address all the channels with a single MRR. We compare and demonstrate two

MRR designs: a small ring with a FSR seven times wider than the required ITU channel grid

of 100 GHz and a large ring with a FSR in close proximity to the required channel grid spacing.

Hence a tunable transmitter can be implemented by combining several small rings or with only

one large ring.

4.1 Small 4-port add-drop racetrack resonator

4.1.1 Design, Simulation and Optimization

With the goal of designing an economically viable ring filter for the CML, a low-loss SiN

waveguide based compact racetrack-resonator is demonstrated. A square SiN waveguide with

dimensions of 400 nm (width) x 400 nm (height) is used. These dimensions provide a good

confinement of the light and are selected as per the fabrication recipe of our industrial partner.

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These ring-resonators are fabricated over a standard Si-wafer where the SiN structures are

deposited over a 4 μm thick SiO2 BOX layer and covered with a 4 μm thick SiO2 clad over it.

At a wavelength of 1550 nm, the refractive index of the SiN is considered to be 2.0458 and for

the SiO2 is 1.45. The effective refractive index ‘neff’ and the group index ‘ng’ are evaluated

using the Eigenmode solver in Lumerical MODE via FDE method. The calculated neff for the

fundamental TE and TM modes are 1.488701 and 1.488146, respectively. Whereas, their

corresponding group indices ng are 1.761564 and 1.7713, respectively. The neff and the ng

dependence on wavelength can be seen in Figure 4.3, which shows that at higher wavelengths,

neff and ng decreases.

The waveguide fabrication tolerance can be studied from Figure 4.4, where we can see the

effect of changing the width and the thickness of the waveguide over the neff. This helps in

understanding the fabrication sensitivity of the waveguide and its impact on device

performance. If the thickness of the waveguide is fixed at 400 nm and the waveguide width is

(a)

(b) (c)

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(d) (e)

Figure 4.3 (a) Perspective view of a Si3N4 channel waveguide with insets showing the cross-section waveguide geometry and fundamental TE & TM mode distribution; (b) Wavelength dependent effective index for TE mode (c) Wavelength dependent group index for TE mode

(d) Wavelength dependent effective index for TM mode (e) Wavelength dependent group index for TM mode

varied (Figure 4.4 (a)), then below 228 nm or above 398 nm, the mode with higher neff will be

TE mode. If the waveguide width is selected in between the above-mentioned range, then the

TM mode has higher neff. On the other hand, if the waveguide width is fixed at 400 nm and the

thickness varies (Figure 4.4 (b)), then after 404 nm the TM mode has higher neff than TE mode.

(a) (b)

Figure 4.4 The fabrication tolerance showing the change in the neff of fundamental TE and

TM mode at 1550 nm due to (a) variation in the width (fixed thickness at 400 nm) (b) variation in the thickness (fixed width at 400 nm)

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Whereas, below this thickness, TE mode has higher neff than TM mode. Also, if waveguide

width or thickness is chosen to be below 180 nm then modes are no longer confined within the

waveguide and they tend to diffuse inside cladding. This change in the neff of the fundamental

mode due to the change in the waveguide dimensions allows us to study the impact on output

performance metrics of the device such as FSR, 3-dB bandwidth and Q-factor.

To design the racetrack-resonators, the design parameters were selected on the basis of the

supermode analysis as discussed in section 2.1. The first two eigenmodes of the directional

coupler are evaluated using a finite element mode solver in Lumerical MODE. An optimum

field coupling coefficient κ is chosen so as to have the critical coupling condition. A selection

of κ is done using a MATLAB code for designing an add-drop ring resonator (shown in

Appendix IV). The optimum κ value helps in deciding the other design parameters such as the

coupling gap and the coupling length. The coupling length considered here is simply the length

of the two identical parallel waveguides. As the value of κ changes, accordingly the coupling

gap also changes which determines the optimum coupling condition at the coupling region.

The dependence of κ over the coupling gaps can be seen in Figure 4.5 for different coupling

lengths of 5 μm, 10 μm, 15 μm and 20 μm for a waveguide of dimensions 400 nm x 400 nm.

Figure 4.5 Field coupling coefficient ‘κ’ vs gap, λ=1550 nm, coupler length L=5 μm, L=10 μm, L=15 μm and L=20 μm, 400 nm x 400 nm waveguide, calculated

using the waveguide mode solver with a 10 nm mesh size

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The coupling gap is an important parameter to obtain the critical coupling condition and for

the ring to behave as a perfect resonator, the dependence of the two supermodes on the coupling

gap is also shown in Figure 4.6. This plot shows how the coupling behaviour varies if the

coupling gap changes due to the fabrication discrepancies. The neff of the first two Eigen modes

(symmetric and antisymmetric modes) calculated at a wavelength of 1550 nm for a coupling

gap of 460 nm are 1.517327 and 1.448628 respectively, and for a coupling gap of 900 nm is

1.500668 and 1.470932, respectively. These effective refractive indices are used to model two

different racetrack resonators presented further and to determine the output performance

metrics of these device such as FSR, 3-dB bandwidth and Q-factor. The bending radius of the

rings are selected to minimize bending losses for the 400 nm x 400 nm waveguide which can

be seen in Figure 4.7 for a 900 bend. The coupling length and the radius are selected to obtain

a specific path length so as to have the required FSR. Type A racetrack resonator has a total

optical path length of 602.11 μm and type B has a total optical path length of 315.56 μm. The

κ is chosen to have a high drop port peak intensity and to obtain a critical coupling condition

with the minimal 3-dB bandwidth using the transfer function equations in MATLAB

(Appendix IV). The selected κ helps in determining the design parameters of ring resonators

Figure 4.6 The neff of symmetric and antisymmetric modes versus the coupling gap, λ= 1550 nm, 400 nm x 400 nm Si3N4 waveguide

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Figure 4.7 Waveguide bend loss vs. radius for 400 nm wide SiN waveguide (in dB scale), bend angle of 900

such as g and Lc using equations (2.5) – (2.8). The waveguide propagation loss included in the

simulations is 1 dB/cm (Bauters et. al, 2011). Both filters are designed to target the central

resonant wavelength (λo) of 1550 nm. The optimum design parameters for the modelling and

simulation of both types of racetrack resonators are listed in Table 4.1. These parameters are

used to simulate the structure in 2.5D-FDTD solver to obtain accurate optical response.

The schematic for both the designs are seen in Figure 4.8. The optical power attenuation

coefficient ‘α’ is considered to be 1 [/cm]. The simulated optical response of type A and type

B are shown in Figure 4.9 and 4.10, respectively. The attributes from the simulated responses

are presented in Table 4.2. The FSR obtained for type A ring filter is 2.34 nm (~291 GHz)

which is almost three times the channel spacing and for the type B is 4.57 nm (~568.40 GHz)

which is more than five times the channel spacing. The targeted resonant wavelength is near

1550 nm with a high ER for both the designs.

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Table 4.1 Design parameters for two different racetrack-resonators

Parameters R (μm) L (μm) Gap (nm) (κ) λo (nm) Type A 90 18.31 460 0.1699 1550 Type B 50 0.7 900 0.2 1550.34

Figure 4.8 The schematic design of two different racetrack resonators (a) Type A, (b) Type B

(a)

(b)

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Figure 4.9 Simulated optical response for type A racetrack-resonator

Figure 4.10 Simulated optical response for type B racetrack-resonator

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Table 4.2 Performance attributes for two different racetrack-resonators

Parameters FSR (nm) FWHM (nm)

ER (dB) Q-factor Finesse λo (nm)

Type A 2.34 0.0074 60.96 209386 316.21 1549.46 Type B 4.57 0.0151 35.79 102671 302.65 1550.34

Figure 4.11 The intensity profile of the light propagating inside the racetrack resonator obtained using 2.5D-FDTD simulations in Lumerical MODE.

The drop port peak intensities for both the rings is around ~93% of the total input light power

which shows that there is still scattering losses in the FDTD simulations. Figure 4.11 shows

the intensity profile of the light propagating inside the ring and some scattering losses as well.

It is in an on-resonance state, showing the extraction of all the resonant wavelengths at the

drop port from the light injected at the input port, leaving no transmission at the through port.

4.1.2 Fabrication, Measurements and Analysis

For the fabrication of these devices, the layout was made in the K-layout software. The mask

dimensions for the straight and the curved waveguides is 400 nm (wide) x 400 nm (height).

The total chip size is 1.6 cm x 3.58 cm. Few replicas of the main design are proposed along

with some variations in the gaps of the coupling regions and the waveguide widths. Due to the

75

fabrication discrepancies, these design variations allow a possibility of achieving at-least one

working device with the desired output spectral response. No grating couplers or tapers are

used at the end of the devices and therefore, light from the input fiber is coupled directly to the

waveguide edge facet. The devices were fabricated using the process flow described in the

section 3.3.2, where instead of a LPCVD, we have used a PECVD technique for the Si3N4

deposition as per the requirement of the research group. The propagation loss measured for the

deposited waveguide is around ~0.4 dB/cm. Only type A racetrack-resonator devices were

measured using the optical test setup (described in section 3.3.3). Type B devices were

fabricated but could not be measured due to time constraints. The proper transmission peaks

were observed for the devices only at the through port. At the drop port, no proper transmission

peaks were measured, instead noise was obtained. This could be due to the high scattering,

propagating or coupling losses induced due to the improper coupling gap regions, variation in

the waveguide widths and sidewall roughness of the waveguides. The measured transmission

response at the through port and the curve-fit for one of the device can be seen in Figure 4.12.

This curve fit is nothing but the smoothness of the measured response where the actual device

signal is extracted and differentiated from the overall noise due to the setup. Noise can be seen

in the measured response which is possibly due to the slight vibration observed in the optical

test setup and the noise of the instruments itself. Isolating the optical stage along with both

input and output fibres could possibly resolve the issue of noise while performing

measurements. Moreover, there is a drift observed in the transmission response of the device

which is due to a shift in the test setup while running the wavelength sweep. The obtained FSR

is around ~5.76 nm which is higher than the theoretical value of 2.34 nm. This increase in the

FSR could possibly be due the difference in the fabricated waveguide dimensions as the

waveguide width has reduced by almost ~40 nm. This reduction in the waveguide width

reduces the neff thereby increasing the FSR (from eqn. 2.20) and so the obtained value holds

true as per theory. The obtained neff of the fabricated waveguide has reduced from 1.4889 to

1.4752 and the ng has reduced from the 1.762 to 1.6975. This reduction in ng due to decrease

in width of the waveguide has increased the FSR which was validated by simulating the RR

using the fabricated dimensions. Although, the change in the thickness of the core waveguide

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Figure 4.12 Transmission spectra for a small ring filter, waveguide 400 nm x 400 nm

was not taken into consideration. The ER obtained is around ~17.21 dB which is well above

the desired ER (of 10dB) required for the use in DWDM applications. The measured FWHM

is approximately 0.45 nm giving a Q-factor of around 3444 which are low as compared to the

simulated results. The SEM image of the fabricated RR and its coupling region is shown in

Figure 4.13 where the coupling gap is seen higher than the designed value by ~30 nm and the

waveguide widths are off by ~40 nm. The possible explanation for no output at the drop port

could be due to the variation in the coupling gap region which leads to under-coupling,

scattering losses due to the sidewall roughness and the propagation losses of the fabricated

waveguide. The low peak sharpness and high 3-db bandwidth could possibly be due to

reduction in the neff of the waveguide. This reduction in neff has increased the 3-dB bandwidth

which in turn has reduced the Q-factor of the fabricated device. Also, the central resonant

wavelength (λo) is shifted to 1549.84 nm since the neff has reduced due to change in the

fabricated dimensions (from eqn. 2.1). In order to fabricate these filters with dimensional

accuracy, some iterations need to be made in the design in future taking into account the

fabrication discrepancies. The FSR of the designed filter is much larger than the required

channel grid recommended by ITU. But several of these ring filters can be used, as transmissive

filters, to remove the chirp of a tunable laser tuned electromechanically via MEMS actuators

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(a)

(b)

Figure 4.13 SEM image of (a) the fabricated RR and (b) the coupling region of RR showing

variation in the gap and the waveguide widths

(setup as shown in Figure 3.1). The transmitted signal from the tunable laser is focused on one

of the many transmissive ring filters each corresponding to a different wavelength channel. To

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change the wavelength channel, potential is applied to the electrostatic actuator which in turn

rotates the MEMS mirror thus allowing to choose the different filters. This selection of

different channels will attenuate the ‘0’ data bits and allow only ‘1’ data bits to pass through,

thus removing the chirp of a tunable laser.

4.2 Large 4-port add-drop racetrack resonator

4.2.1 Design, Simulation and Optimization

In this section we present a novel method for developing a tunable transmitter by using a Si3N4

waveguide based large racetrack resonator filter with a FSR matching the ITU channel grid

required for the NG-PON2 systems. With an aim of achieving an economical approach, a low

loss SiN ring filter is demonstrated using a CMOS compatible process. The channel waveguide

has a square dimension of 435 nm x 435 nm (as seen in Figure 3.3 (a)) giving a good

confinement of the light. These dimensions are selected in accordance with our industrial

partner so as to match their fabrication process. These nitride ring filters are fabricated over a

4 μm thick SiO2 layer on a standard Si wafer, cladded by a 4 μm thick oxide over it. The

refractive indices of the Si3N4 and the SiO2 at 1550 nm are considered to be 2.0458 and 1.45,

respectively. The effective refractive indices neff and the group indices ng are calculated using

the FDE method via Eigenmode solver for the fundamental TE and TM modes. The obtained

neff for the fundamental TE and TM mode for a straight waveguide are 1.51236 and 1.51217

and their corresponding group indices are 1.8616 & 1.8666, respectively. The neff and ng are

wavelength dependent and their dependency can be seen in chapter 3 in Figure 3.3 (b) and (c)

respectively.

The design approach, as discussed in the section 3.2.2, is based on the initial design of the

directional coupler using CMT. Based on the CMT, all the desired coupling parameters are

calculated using the analytical equations as discussed in section 2.1. At first, an optimum κ is

selected using the analytical equations shown in the MATLAB code for designing a RR

(Appendix IV). The waveguide propagation loss considered in simulations is 1 dB/cm (Bauters

79

et al., 2011). To obtain a critical coupling condition, the coupling losses are included in

simulation equal to the cavity losses given by t = |t|exp(jφt), where |t| represents the coupling

Figure 4.14 Field coupling coefficient ‘κ’ vs gap, λ=1550 nm, coupler length L=10 μm, L=15 μm, L=20 μm, L=25, L=30 μm and L=35 μm, 435 nm x 435 nm

waveguide, calculated using the waveguide mode solver with a 10 nm mesh size

losses and φt represents the phase of the coupler. The value of κ is chosen to have high drop

port peak intensity with a minimal 3-dB bandwidth possible. The κ is an important factor in

deciding an optimum coupling region and helps in choosing the design parameters such as

coupling gap (g) and coupling length (L). A general trend of an exponential decrease in the κ

with the increasing gap can be seen in Figure 4.14 for the selected waveguide dimensions as

function of coupling lengths. The chosen κ is 0.4645 giving a drop port peak intensity around

99% of the total input power, targeted for λ0 near 1550 nm. The coupling length in our design

consists of two parallel waveguides only (excluding bends) and the power behaviour within a

directional coupler can be expressed as a function of the structure of the coupler, position of

the coupler, the coupling coefficients and the power transmission ratio. The neff of the

symmetric and antisymmetric modes evaluated using the FDE method are 1.552085 and

1.462307, respectively for the selected directional coupler gap of 350 nm. The change of these

effective refractive indices as a function of coupling gaps is shown in previous chapter in

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Figure 4.15 The general schematic design of a large racetrack resonator

Figure 3.6 (a). A total optical path length of 1768 μm is chosen in order to obtain a desired

FSR of 100 GHz (0.8 nm), comprising of ring radius (r) of 230 μm, coupling length (L) of 35

μm and two straight waveguides each of length 126.435 μm. Using equation (2.9), the required

L is obtained to be 35 μm depending upon optimum κ and chosen g. The design is simulated

in 2.5D-FDTD using Lumerical MODE whose general schematic can be seen in Figure 4.15.

A simulated spectral response shown in Figure 4.16 gives the desired FSR of 0.8 nm with the

λ0 at 1550.17 nm which is close to the target wavelength of 1550 nm. The ER obtained is

around ~26 dB for the central resonant wavelength. We have obtained a narrow 3-dB

bandwidth of 0.0126 nm giving a sharp resonant peak with a Q-factor of 123,029. Another

important characteristic is Finesse which is calculated to be 63.49. This single large ring-filter

can be used as an external filter in the CML for the NG-PON2 systems as its FSR matches the

ITU channel grid.

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Figure 4.16 Simulated optical spectra of a large racetrack resonator showing transmission at the drop port and the through port (in dB)

To validate that the designed racetrack resonator (as an external filter) aids in improving the

ER of the DML, circuit simulations are carried out using Lumerical Interconnect. A circuit

simulation schematic in Figure 4.17 shows four different configurations, wherein firstly, a

DML signal is sent directly to an EYE diagram analyser which can perform a comprehensive

set of measurements on the time domain waveform (Figure 4.17 (1)). Secondly, a DML laser

is sent through a 20 Km long fiber.to an EYE analyser (Figure 4.17 (2)) which gives the ER

without a filter. In a third configuration, the DML signal is sent through a racetrack resonator

filter designed for a 100 GHz FSR directly into the EYE diagram analyser (Figure 4.17 (3)),

which should aid in increasing the ER of the laser. In the fourth configuration, the DML signal

is transmitted through a ring filter which is further sent through a long fiber (20 km) going into

an EYE diagram analyser (Figure 4.17 (4)) to verify the effect on the ER as the data signal

transmits over a long distance through a fiber. In configuration (1), the EYE filter analyser

gives a low ER of 2.97 dB. In configuration (2), the optical signal from the DML is sent just

through a 20 Km long optical fiber giving a slightly reduced ER of 2.95 dB which is due to the

signal degradation because of the interaction of the frequency chirp with the chromatic

dispersion of the fiber. In configuration (3), the DML signal is transmitted through a designed

ring filter giving an increased ER of 10.65 dB. This increase in the ER of the DML signal (in

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comparison to the configuration (1)) is due to the attenuation of the red-shifted ‘0’ data bits of

the signal allowing only the blue-shifted ‘1’ bits to pass. This is done by aligning the laser

wavelength on the transmission edge of an OSR, which in this case is the above designed

Figure 4.17 A general schematic of the circuit simulation setup in the Lumerical Interconnect showing 4 different configurations

racetrack resonator. The laser wavelength is set at 1550.27 nm. An ER of around ~8.81 dB is

obtained from the EYE analyser in configuration (4) which is higher compared to the

configuration (2) but lower than (3) due to the interaction of the chirp with the chromatic

dispersion of the fiber. For the configuration (3), the obtained ER is plotted in Figure 4.18

versus the detuning of the wavelength (Δλ) for a span of ±1 nm. It shows an increase in the ER

of the DML at the wavelengths similar to the resonant wavelengths of the ring filter which

occurs by the virtue of aligning the laser wavelength (1550.27 nm) on the transmission edge

of the racetrack resonator filter. We observe a high ER of 10.65 dB at a span of ±0.8 nm

corresponding to the FSR of the filter. But, we also observe two peaks at ±0.4 nm giving even

a higher ER of 18.5 dB. The possible explanation for this could be that at ±0.4 nm the ‘0’ bits

are completely attenuated whereas ‘1’ bits are not and are allowed to pass. Whereas, at ±0.8

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Figure 4.18 Plot showing ER (in dB scale) vs. detuning (Δλ) for configuration (3)

nm, ‘1’ bits are more attenuated than ‘0’ bits resulting in an inversion of the bit pattern which

can be seen in Figure 4.19 where the waveform for signal amplitudes are compared and

measured using an oscilloscope directly from the laser and after the light has propagated

through the ring filter. Thus, higher ER of around 18.5 dB is obtained due to the complete

Figure 4.19 Graph showing pulse amplitude from the laser (red line) and the comparison of pulse amplitudes after the propagation through ring filter for lower ER

(blue dashed line) and higher ER (black dashed line) obtained

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Figure 4.20 Power spectrum as a function of frequency (THz) showing adiabatic chirp

attenuation of ‘0’ bits without attenuating ‘1’ bits. Whereas, other ER of around 10.65 dB is

obtained when ‘1’ bits are also attenuated along with ‘0’ bits. The distortions in the pulses after

passing through the filter is due to the gain-saturation-induced self-phase modulation (SPM)

(Agrawal & Olsson, 1989). An adiabatic chirp of the DML used in the circuit simulations is

30 GHz shown in Figure 4.20. These circuit simulations show and validate the use of a

designed racetrack resonator as an external filter in front of the DML (which in our case will

be a tunable laser) in order to develop an alternative transmitter, increasing the range of the

transmission.

4.2.2 Fabrication, Measurements and Analysis

For the fabrication of this large racetrack resonator, the mask layout is made in the K-layout

software with the straight and the curved waveguide mask dimension of 435 nm width. The

total chip area is 1.5 cm x 2 cm. Some design variations are proposed so as to mitigate the

fabrication discrepancies and to achieve at least one working device giving a desired spectral

response. They are designed such that the light couples directly from the input fibre to the

waveguide edge facet. The fabrication process flow of these devices is already presented above

in section 3.3.2 to match the fabrication criteria of our industrial partner.

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Figure 4.21 Measured spectra showing the transmission at the through and the drop port for a large racetrack resonator

These large racetrack-resonator devices were measured using the optical test setup described

in section 3.3.3 where only the fundamental TE mode is excited and the polarization is

maintained using the polarization controller. The measured output spectral response at the

through and the drop port is shown in Figure 4.21. The measured FSR is 0.75 nm between the

two resonant wavelengths at 1549.87 nm and 1550.62 nm. The FSR differs from the theoretical

value probably due to the change in the ng and neff caused by the difference in the fabricated

waveguide dimensions. The obtained ER of the device is 15.14 dB which is less than the

theoretical value. The 3-dB bandwidth at 1549.87 nm is 0.064 nm, corresponding to a high Q

of 24,217. The Finesse of the device is measured around 11.71. The SEM image of the

measured device in Figure 4.22 shows that the waveguide widths have reduced by almost 30

nm and that the gap has increased by almost 40 nm. Therefore, the reduction in the 3-dB

bandwidth and the Q-factor could be due to this increase in the coupling gap, which in turn has

reduced the κ and neff (from eqn. 2.22 and 2.24). The ER of the drop port peak intensities are

low as compared to the simulated values. A reason for this could be the decrease of κ which in

turn has reduced the mode amplitude in the drop port waveguide. A normalized through port

transmission curve, shown in Figure 4.23, compares the measured and the simulated response

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Figure 4.22 SEM image of a directional coupler of a fabricated large RR

Figure 4.23 Normalized transmission spectra (in dB) showing the simulated and the measured through port response

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which shows a blue-shift in the resonant wavelength λ0. This holds true since the neff has

reduced, thereby, reducing the λo (from eqn. 2.1). The measured insertion loss of the fabricated

device is around ~6 dB. Using equation 2.2, the measured ng of the fabricated waveguide is

1.8115 which is lower than the simulated value of 1.8625 which effects the device

performance. Also, the thickness of the waveguide has increased by 5% which has more effect

on the device output as compared to the waveguide width, which can be studied from the plots

in Figure 3.24. Therefore, to mitigate the fabrication discrepancies, some iterations will be

done in future designs based on the performance of the devices and other data obtained.

4.3 Summary

To summarize, we demonstrate a small and a large Si3N4 waveguide racetrack resonator to be

used as an external filter in front of the tunable laser to attenuate the adiabatic chirp of the

laser. When the laser wavelength is aligned on the transmission edge of the ring filter, data bits

‘0’ are attenuated while data bits ‘1’ are allowed to pass through. This will aid in increasing

the ER, thereby increasing the transmission range of the data signal coming from the tunable

laser, which will be used in future for implementing the CML. A small racetrack resonator of

waveguide dimensions 400 nm x 400 nm gives a FSR of 5.76 nm. The λo has shifted to 1549.84

nm, measuring a 3-dB bandwidth of approx. 0.45 nm giving a Q-factor of around 3444. The

ER of the device is measured to be around 17.21 dB which is large enough to be used in

realizing CML. The measured FSR of the ring filter is almost 7 times the required ITU channel

grid. Hence in order to be used for a tunable transmitter, several small rings can be used in

front of the tunable laser each corresponding to a particular wavelength channel. The

wavelength channel selection will be done using MEMS actuation, thereby attenuating the

adiabatic chirp of the tunable laser.

Also, we have demonstrated a large racetrack resonator filter made of Si3N4 waveguide with a

FSR of 0.75 nm (93.58 GHz) aiming to match the ITU channel grid of 100 GHz spacing.

However, the measured FSR is off by 0.05 nm from the desired value of 0.8 nm. The obtained

ER is 15.14 dB with a Finesse of 11.71. The measured 3-dB bandwidth at λ0 (1549.87 nm) is

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0.064 nm giving a Q-factor of 24,217. The interconnect simulations show an enhancement in

the ER of the DML from 2.97 dB to almost 18.5 dB by the use of the designed ring filter. Some

iterations will be done in the future design to mitigate the fabrication challenges, thereby,

obtaining the desired FSR of 100 GHz. Therefore, in future, the designed RR allows the

possibility to demonstrate a novel cost-effective and a compact alternative transmitter

technology for the NG-PON2 systems.

CONCLUSIONS AND FUTURE WORK

In summary, we have studied, in theory and experiment, the racetrack-resonators in different

configurations and in different waveguide geometries. The photonic ring filters based on Si3N4

waveguide platform have been designed, simulated and characterized. The filters demonstrated

using a CMOS compatible platform include:

• A photonic ring reflector constituting of a ring having a radius of 35 μm, integrated

with Y-splitters to form a reflector configuration. It gives a measured FSR of 6.03 nm

with a Q of 1122.82 at λ near 1550 nm with an aim of targeting a wide FSR to be used

potentially in tunable lasers.

• A small RR filter with the radius of 90 μm giving a FSR of 5.76 nm, FWHM of 0.45

nm, a Q of 3444 and a high ER of 17.21 dB. This designed small RR filter gives a FSR

seven times the channel spacing of the ITU-channel grid of 100 GHz. This compact

and cost-effective RR has a potential application in implementing a tunable transmitter

by using several such RR’s in front of the tunable laser, each corresponding to a

different wavelength channel. Then the chirp of the tunable laser will be attenuated by

aligning the laser wavelength to one of the many RR wavelengths using channel

selection mechanism, thereby, increasing the transmission range of the signal by

increasing the ER of the laser.

• A large Si3N4 RR filter with an optical path length of 1768 μm giving a FSR of 0.75

nm, a high ER of 15.14 dB, a 3-dB bandwidth of 0.064 nm at 1549.87 nm and a high

Q-factor of 24,217. A simulated response gives the desired 100 GHz FSR and high ER

of 26 dB but due to fabrication discrepancies the measured values differs. This

demonstrated RR filter provides a novel platform for developing a tunable transmitter

by acting as an external filter in front of the tunable laser. Our platform of Si3N4

photonics provide a cost-effective approach towards developing a CML as compared

to the other concepts presented in the literature, wherein instead of thermal tuning we

will potentially use electromechanical tuning using MEMS actuators which uses less

power

90

Interconnect simulations have been presented in the thesis for the designed large RR filter

which shows an enhancement in the ER of the DML from 2.97 dB to almost 18.5 dB. Also, a

novel Si waveguide based serially coupled 3rd order ring filter in the reflector configuration

has been designed and simulated showing an extended FSR of 90.2 nm wide enough to cover

the entire C or L-band. The Vernier effect is used to achieve a wide FSR using three ring-

resonators of different optical path lengths. The spectral response of the device shows an

interstitial peak suppression of 7.6 dB with no dominant resonance peak splitting. The

important factors concerning design improvement are discussed and compared with the work

of the other research groups. To the best of our knowledge, the ring reflector design achieved

by integrating a cascaded 3-ring filter along with the Y-splitters is unique and novel in

comparison to the ring reflectors reported by other research groups.

In future, the Si 3rd order ring reflector will be optimized further by carefully selecting co-

prime integer multiples of the FSRs and by optimizing the κ values for every coupling region.

Similarly, the Si3N4 ring reflector presented in the thesis will be optimized in future to develop

a higher order ring reflector. Some iterations in the actual design will be carried out along with

the changes required in the fabrication process flow to achieve the device dimensions with high

precision. As we have encountered approximately ±40 nm variation in the fabricated

waveguide widths and the coupling regions of the RR. So, to mitigate them in the future, the

bias of ±40 nm and ±80 nm will be applied to the design layout to compensate the variation in

the performance attributes of the devices obtained due to changes in the neff and ng of the

waveguides. Also, in future simulations, the bends will also be included while considering

optimum κ so as to include the effect of bending region. These photonic ring reflectors, once

fabricated, will be promising for a wavelength channel selection system in a tunable laser. In

a similar manner, iterations will be done on future designs of the small and the large Si3N4 RR

so as to mitigate fabrication discrepancies and thus obtaining the desired FSR. The large RR,

once fabricated with the exact waveguide dimensions and the coupling gap precision, will give

a FSR matching the ITU channel grid spacing of 100 GHz. It has a potential application in

realizing a CML operational in burst mode for TWDM in NG-PON2 systems.

APPENDIX I

Derivation for power equations of racetrack resonator

As discussed in Section 2.1, all mode amplitudes depend on the factor ‘θ’ which is equal to ωL/c. Where ‘L’ is the circumference of the ring given by L=2πr. ‘r’ is the ring radius measured from the ring center to the center of the waveguide, c=co/neff is the phase velocity of the ring mode and ω=kco is the angular frequency, where co refers to the vacuum speed of light. ‘k’ is the vacuum wave number related to the wavelength ‘λ’ by relation:

= (A I-1)

Taken from Rabus (2007) Using this wave number, the effective refractive index ‘neff’ can be introduced within the ring relations as:

= . = . (A I-2)

Taken from Rabus (2007) where β is the propagation constant. Thus, the value of θ is then given by the relation:

= . = . . = . . 2 = . . = 4 (A I-3)

Taken from Rabus (2007) Since, all the complex mode amplitudes E are normalized, so that their squared magnitude corresponds to the modal power. Thus the power transmission Pt1 in the output waveguide is then given by:

Pt1 = |Et1|2 =| | | | ( )| | | | ( ) (A I-4)

Taken from Rabus (2007) where t = |t|.exp(j ), |t| represent the coupling losses and represents the phase of the coupler. The circulating power Pi2 in the ring is given by:

Pi2 = |Ei2|2 =

( | | )| | | | ( ) (A I-5)

Taken from Rabus (2007) On resonance, ( + ) = 2πm, where m is an integer. Then the above relations of the notch filter can be written as follows:

92

Pt1 = |Et1|2 =( | |)( | |) (A I-6)

Pi2 = |Ei2|2 =

( | | )( | |) (A I-7)

Taken from Rabus (2007) and at resonance, the output power from the drop waveguide in the 4-port add-drop filter is written as:

Pt2 = |Et2|2 =

| | . | | .( | |) (A I-8)

Taken from Rabus (2007)

The through port mode amplitude Et1 will be zero at resonance for identical symmetrical couplers t1 = t2 at α=1, which shows that the wavelength at resonance is fully extracted by the resonator. The value of loss coefficient α=1 can only be achieved by implementing the gain incorporated inside the ring resonator to compensate the waveguide losses. The possibility of achieving the condition of output power from the through waveguide, Pt1=0, is only by adjusting the coupling parameters t1, t2 to the loss coefficient α (i.e. α=|t1|/|t2|)

The derivation of the FWHM or 3-dB bandwidth

Using the expression of the drop port eqn. (2.9) and the corresponding above eqn. of Pt2, we have:

∗ / /∗ ∗ = | | | |( | |) (A I-9)

Taken from Rabus (2007)

Assuming that the coupling coefficients are real, lossless, and without a phase term then the above eqn. can be written as:

( )( ) ( ) = ( )( ) (A I-10)

Taken from Rabus (2007) Then, 2(1 − ) = 1 − 2 Cos( ) + ( ) (A I-11)

Taken from Rabus (2007) For small θ, using the real part of the series expansion of the Euler formula Cos(θ) = 1 – θ2/2 and so we have,

= ( ) (A I-12)

93

Taken from Rabus (2007) Which can be further reduced to, θ = 1-t2 / t. In the wavelength domain it can then be written as:

2 Δ = (A I-13)

Taken from Rabus (2007) The expression which is commonly used can be obtained by assuming weak coupling and λ >> δλ, then

= 2δλ = (A I-14)

Taken from Rabus (2007)

APPENDIX II

Derivation of transfer equations for 3rd order ring filter

In order to derive the transfer function for the through port for a serially coupled three ring resonator, different individual loop gains are considered. There are six individual loop gains and are expressed as (Chaichuay et al., 2009): = √ √ = √ (A II-1) = √ √ = √ (A II-2) = √ √ = √ (A II-3) = √ (− )√ √ (− )√ = − ( ) (A II-4) = √ (− )√ √ (− )√ = − ( ) (A II-5) = (− ) (− ) (− ) (− ) = ( ) (A II-6)

There are five possible products of transmittance for two separate loops (i.e. the loops which have no node in common) given by (Chaichuay et al., 2009): = ( ) (A II-7) = ( ) (A II-8) = ( ) (A II-9) = − ( ) (A II-10) = − ( ) (A II-11)

Also, there is one possible product of transmittance of three separate loops, given by (Chaichuay et al., 2009): = ( ) (A II-12)

APPENDIX III

Derivation of relation between effective refractive index n(r,ϕ) and field function (ψ)

For a homogeneous microdisk resonator having radius R, the effective refractive index n(r,ϕ) = n if r < R and inside the microdisk Eqs. 2.1 and 2.3 take the form

+ + + ( , ) = 0 (A.III-1)

Taken from Dettmann (2008) where ψ is either equal to Ez or Hz, depending upon the polarization. The surrounding refractive index is fixed to n=1. Separation of variables and physical conditions in the middle of the disk and at infinity lead to the field function ψ of the form:

ψ = ( ) , r < R ( ) , r > R (A.III-2)

Taken from Dettmann (2008)

where, Jm and Hm are Bessel and Hankel functions of the first kind respectively and m is the azimuthal modal index. Then the boundary conditions (continuity of the EM fields) at the point r=R lead to a set of the independent transcendental equations for the microdisk resonances ( ) ( ) − ( ) ( ) = 0 (A III-3)

Taken from Dettmann (2008) where β=n for TM modes and β=1/n for TE modes. The radial modal index ‘q’ is used to label different resonances with the same azimuthal index ‘m’ On the basis of self joint extension theory (Zorbas, 1980) (Shigehara, 1994) (Sieber, 2007) it is shown that resonances of a homogeneous microdisk of radius R with a point scatterer of strength a located at the distance d < R with the corresponding local coordinates (d, ) are defined by the transcendental equation

0 = − − − ∑ ∈ ( ) (A III-4)

Taken from Dettmann (2008) where =0.5772 is the Euler-Mascheroni constant, ∈ = 2 if m≠0, ∈ =1 if m = 0 , and = ( ) ( ) − ( ) ( ) (A III-5) = ( ) ( ) − ( ) ( ) (A III-6)

Taken from Dettmann (2008)

98

The field function ψ is then of the form

Ψ = N − ( | − |) + ∑ ∈ ( ) ( ) ( ),∑ ∈ ( ) ( ) ( ), (A III-7)

Taken from Dettmann (2008) where N is a normalization factor and r< (r>) is the smaller (larger) of r and d

APPENDIX IV

MATLAB script for computing optical response of ring-resonator

% RingResonator.m: Ring Resonator spectrum function [Ethru, Edrop]=RingResonator (lambda, Filter_type, r, Lc, k) % lambda: wavelength (can be a 1D array) in meters % type: "all-pass" or "add-drop" % r: radius % Lc: coupler length lambda=(1500:0.001:1600)*1e-9; % wavelength range Filter_type='add-drop'; r=90e-6; Lc=18.31e-6; k=0.1696; t=sqrt(1-k^2); %coupling coefficients neff = neff_lambda(lambda); alpha_wg_dB=1; % optical loss of optical waveguide, in dB/cm alpha_wg=-log(10^(-alpha_wg_dB/10));% converted to /cm L_rt=Lc*2+2*pi*r; phi_rt=(2*pi./lambda).*neff*L_rt; % beta = propagation constant A=exp(-alpha_wg*100*L_rt); % round-trip optical power attenuation alpha_av=-log(A)/L_rt; % average loss of the cavity if (Filter_type=='all-pass') Ethru=(-sqrt(A)+t*exp(-1i*phi_rt)) ./ (-sqrt(A)*conj(t)+exp(-1i*phi_rt)); Edrop=zeros(1,length(lambda)); elseif (Filter_type=='add-drop') % symmetrically coupled Ethru=(t-conj(t)*sqrt(A)*exp(1i*phi_rt)) ./ (1-sqrt(A)*conj(t)^2*exp(1i*phi_rt)); Edrop=-conj(k)*k*sqrt(sqrt(A)*exp(1i*phi_rt)) ./ (1-sqrt(A)*conj(t)^2*exp(1i*phi_rt)); else error(1, 'The''Filter_type'' has to be ''all-pass'' or ''add-drop''.\n'); end plot (lambda, [abs(Ethru); abs(Edrop)]) hold on function [neff]=neff_lambda(lambda) neff = 1.5180 - 0.85*(lambda*1e-9-1.55); % neff of the used waveguide

APPENDIX V

MATLAB script for computing of cut-off thickness Taken from (Gang, 2005) nf=2.0458; %R.I. of Si3N4 nc=1.45; %R.I. of cladding (SiO2) ns=1.45; %R.I. of substrate (SiO2) m=0; %TE modes lambda=1.55e-6; %wavelength k0=2*pi/lambda; beta=k0*nf; A=sqrt((ns.^2-nc.^2)/(nf.^2-ns.^2)); tco=(lambda/(2*pi*sqrt(nf.^2-ns.^2)))*((m*pi)+atan(A)) %compute cutoff

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